id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
800,970 | AMR-149-0050 | Open Problems and Questions about Geodesics — Conjecture 51 | In the Lorenzian setting, one can ask to construct all manifolds such that all light-like geodesics are closed, see e.g.\ [Mou-Suh2013, Suhr2013b].
An easier version of the question above is the following conjecture sometimes attributed to Berger:
*Let $(M,g)$ be a closed simply connected manifold such that all geode... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 51
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,971 | AMR-149-0051 | Open Problems and Questions about Geodesics — Question 52 | To the best of our knowledge, the existence of a closed geodesic on a Lorentzian manifold is a quite complicated problem and nothing is known in dimensions $\ge 3$. In dimension 2, a closed orientable manifold with a metric of signature $(+,-)$
is homeomorphic to the torus. By [Suhr2013a], every Lorentzian 2-dimensiona... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 52
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,972 | AMR-149-0052 | Open Problems and Questions about Geodesics — Question 53 | *Can there exist a complete semi-Riemannian metric $g$ and a non-trivial 1-form $\eta$ on a closed manifold such
that for every light-like geodesic $\gamma(t)$
the function $\eta(\dot\gamma(t))$ grows linearly in both directions: i.e. for every light-like geodesic there exist $C_1 \neq 0, C_2 $ such that
$\eta(\dot\gam... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 53
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,973 | AMR-149-0053 | Open Problems and Questions about Geodesics — Question 54 | It is well-known that a closed Riemannian manifold is geodesically complete, in the sense that every geodesic $\gamma:(a,b)\to {M}$ can be extended to a geodesic $\tilde \gamma:\mathbb{R} \to M$ such that $\tilde \gamma|_{(a,b)}= \gamma$. It is also well known that for any indefinite signature there exist metrics on cl... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 54
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,974 | AMR-149-0054 | Open Problems and Questions about Geodesics — Question 55 ([Sanchez2015]) | We refer to the paper [Sanchez2015] for a list of interesting results on this topic and for a list of open questions from which we repeat here only:
*Assume that a compact Lorentzian manifold is globally conformal to a
manifold of constant curvature. Must it be geodesically complete?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 55
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [Sanchez2015] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,975 | AMR-149-0055 | Open Problems and Questions about Geodesics — Question 56 (Bangert) | *Does there exist a Riemannian metric on a closed surface of genus $\ge 2$ whose geodesic flow is completely integrable? * | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 56
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Bangert | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,976 | AMR-149-0056 | Open Problems and Questions about Geodesics — Question 57 (Paternain) | Ma\ n\'e showed that
a Hamiltonian flow on surfaces is generically Anosov or has zero Liouville exponents [Mane1996]. This suggests that an easier version of the above question would be the following
*Is there a Riemannian metric on a closed surface of genus $\ge 2$ whose geodesic flow has zero Liouville entropy?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 57
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Paternain | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,977 | AMR-149-0057 | Open Problems and Questions about Geodesics — Question 58 | *Let $F_1$, $F_2$ be Finsler metrics on a closed surface of genus $\ge 2$. Assume every (unparameterized) $F_1$-geodesic is an $F_2$-geodesic. Must $F_1$ be obtained from $F_2$ by multiplication by a constant and adding a closed form? * | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 58
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,978 | AMR-149-0058 | Open Problems and Questions about Geodesics — Question 59 | The previous question is related to the other questions in this section because of the following observation from [Mat-Top1998]: one can use the second metric to construct an integral of the geodesic flow of the first one. If both metrics are Riemannian, the integral is quadratic in velocities and the affirmative answe... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 59
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,979 | AMR-149-0059 | Open Problems and Questions about Geodesics — Conjecture 60 ([Bo-Ko-Fo1995]) | *If the geodesic flow of
a Riemannian metric on the torus $T^2$ admits an
integral that is polynomial of degree 3 in the velocities, then the metric admits a Killing vector field. * | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 60
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [Bo-Ko-Fo1995] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,980 | AMR-149-0060 | Open Problems and Questions about Geodesics — Conjecture 61 | We ask whether there exists a non-constant smooth
function on the tangent bundle which is constant along every trajectory. It is well known, see e.g.\ [Tabachnikov2005], that a billiard in an ellipse is integrable.
*If the billiard in $\Omega$ is integrable, then the boundary of $\Omega$ is an ellipse. * | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 61
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,981 | AMR-149-0061 | Open Problems and Questions about Geodesics — Question 62 ([Has-Mor1996]) | A $\Theta$-graph is a graph that looks like the Greek
letter ``Theta'': two vertices connected by three edges, see the picture below.
*Does every metric on $S^2$ admit a stationary $\Theta$-graph?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 62
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [Has-Mor1996] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,982 | AMR-149-0062 | Open Problems and Questions about Geodesics — Question 63 (Gromov) | We call a stationary net non-trivial if it has at least one vertex of valency $\ge 3$, in other words if it is not a disjoint union of simple closed geodesics.
*Are non-trivial stationary nets dense on any closed Riemannian surface? In other words, for each non-empty open subset $U$, is there a stationary net intersec... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 63
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Gromov | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,983 | AMR-149-0063 | Open Problems and Questions about Geodesics — Question 64 | *Suppose a closed manifold $(M,g)$ admits a non-zero
$(1,1)$-tensor field that is self-adjoint with respect to $g$, parallel and nilpotent. Does this manifold or its double cover admit a non-zero light-like parallel vector field?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 64
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,984 | AMR-149-0064 | Open Problems and Questions about Geodesics — Problem 65 | Also in the Finsler case parameterized geodesics determine the connection. Note though that in the Finsler geometry the connection is non-linear and actually there are more than one popular and widely used connections. We will call two Finsler
metrics *affinely equivalent* if any
geodesic of the first metric (considere... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Problem 65
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,985 | AMR-149-0065 | Open Problems and Questions about Geodesics — Problem 66 | *Construct a system of scalar invariants of a projective structure
that vanish if and only if there exists (locally, in a neighborhood of almost every point) a metric compatible with a given projective structure.* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Problem 66
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,986 | AMR-149-0066 | Open Problems and Questions about Geodesics — Question 67 | It is known that, in dimension 2, locally, each reversible path structure is metrizable [Alv-Ber2010, Theorem B].
*In dimension $2$, is each irreversible path structure metrizable?
* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 67
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,987 | AMR-149-0067 | Open Problems and Questions about Geodesics — Question 68 | There exist local (the first examples are due already to Lagrange, Beltrami and Dini)
and global examples of non-proportional projectively equivalent metrics. Locally, in the Riemannian case, a complete description of projectively equivalent metrics is due to Levi-Civita [Levi-Civita1896] and in arbitrary signature is ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 68
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,988 | AMR-149-0068 | Open Problems and Questions about Geodesics — Question 69 | In the Finslerian case, the freedom of reconstructing metric from its geodesic can be much higher. For example, adding
any sufficiently small closed 1-form to the Finsler metric
does not change geodesics of this metric. This transformation of the metric was called a * trivial projective change* in [Matveev2013].
*In d... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 69
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,989 | AMR-150-0001 | Open Problems in Mathematical Logic — Problem 1 (Levin, private communications) | Are the following true?
(1) Can every chain of random reals in the Turing degrees
be combined into a single random real?
(2) Can every Turing ideal generated by random reals be
generated by the columns of a single random real? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Levin, private communications | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,990 | AMR-150-0002 | Open Problems in Mathematical Logic — Problem 2 (Levin) | Is it true that, for every $X\subseteq 2^\omega$ with $\mu(X)=1$,
there exists $Y\subseteq 2^\omega$ with $\mu(Y)=1$ such that, for
every chain $B\subseteq Y$, there is some $\alpha\in X$ satisfying
$[B]=[\alpha]$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 2
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Levin | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,991 | AMR-150-0003 | Open Problems in Mathematical Logic — Problem 3 | The class $\mathrm{ML}(\emptyset')$
of $\emptyset'$-random reals, equivalently the class of $2$-random reals,
is a special case.
Is there a chain
$B\subseteq\mathrm{ML}(\emptyset')$
such that
$[B]\neq[\alpha]$
for every $\alpha\in\mathrm{ML}(\emptyset')$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,992 | AMR-150-0004 | Open Problems in Mathematical Logic — Problem 4 | Toward a negative answer to Levin's Problem 1.2, are the following true?
(1) Are there $2$-random reals $x<_T z$ such that
\[
x'\equiv_T z'?
\]
(2) Are there $2$-random reals $x<_T z$ such that
\[
\left|
K(x\upharpoonright n)-K(z\upharpoonright n)
\right|
=
O(1)?
\]
(3) Is there a Turing ideal $B$ generated by a cha... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 4
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,993 | AMR-150-0005 | Open Problems in Mathematical Logic — Problem 5 | Is there an injective one-way function on the reals? More precisely,
is there a partial computable real function $f$ such that
(i) $f$ is injective and preserves randomness,
(ii) the domain of $f$ has positive Lebesgue measure, and
(iii) $f(x)<_T x$
for a positive-measure set of reals $x$ in the domain of $f$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 5
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,994 | AMR-150-0006 | Open Problems in Mathematical Logic — Problem 6 | Let $M$ be a countably infinite $\omega$-categorical structure in a
finite first-order signature, and let
\[
G=\operatorname{Aut}(M),
\]
equipped with the topology of pointwise convergence. Let
$\operatorname{Aut}(G)$ denote the group of continuous automorphisms
of the topological group $G$, and let
\[
\operatorname{Ou... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 6
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,995 | AMR-150-0007 | Open Problems in Mathematical Logic — Problem 7 | \[
J^A(n)\downarrow
\Longrightarrow
J^A(n)\in T_n.
\]
Also recall that
\[
A\le_{LR} B
\iff
\mathrm{MLR}^B\subseteq\mathrm{MLR}^A.
\]
Does $\le_{SJT}$ imply $\le_{LR}$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 7
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,996 | AMR-150-0008 | Open Problems in Mathematical Logic — Problem 8 | \[
A\le_{SJT} B
\iff
\forall Y \omega\text{-c.a. and }Y\in\mathrm{MLR}
\Bigl(
A\le_T B\oplus Y
\Bigr).
\]
Let Rec denote the class of recursive sets.
Is there a $\Pi^0_1$ class $C$ such that $|C\cap \mathrm{Rec}|=\infty$ and $C\cap \mathrm{Rec}$ is maximally almost disjoint among the recursive sets? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 8
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,997 | AMR-150-0009 | Open Problems in Mathematical Logic — Problem 9 | Determine the equivalence classes of quantifier patterns at the
fourth level of the arithmetical hierarchy:
(1) How many $\equiv_m$-equivalence classes of
$\Sigma^0_4$ quantifier patterns are there?
(2) How many $\equiv_m$-equivalence classes of
$\Pi^0_4$ quantifier patterns are there?
(3) How many $\equiv_{dm}$-equ... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 9
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,998 | AMR-150-0010 | Open Problems in Mathematical Logic — Problem 10 | Is there a decision procedure which, given quantifier patterns
\[
\overline{P},\overline{Q}
\in
\{\exists,\forall,\exists^\infty,\forall^\infty\}^{<\omega},
\]
decides whether
\[
\langle\overline{P}\rangle
\leq_m
\langle\overline{Q}\rangle?
\] | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 10
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,999 | AMR-150-0011 | Open Problems in Mathematical Logic — Problem 11 | A set $A\subseteq\mathbb{R}^2$ is called a *Kakeya set* if, for every
$\alpha\in\mathbb{R}$, there exists $C_\alpha\in\mathbb{R}$ such that
\[
y=\alpha x+C_\alpha
\quad\Longrightarrow\quad
(x,y)\in A
\]
for every $(x,y)\in\mathbb{R}^2$. Equivalently,
\[
\bigl\{(x,y)\in\mathbb{R}^2:y=\alpha x+C_\alpha\bigr\}
\subseteq A... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 11
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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801,000 | AMR-150-0012 | Open Problems in Mathematical Logic — Problem 12 | A Kakeya set $A$ is called *minimal* if every proper subset
$B\subsetneq A$ is not a Kakeya set.
Does every Borel Kakeya set $A$ contain a minimal Kakeya set
$B\subseteq A$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 12
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,001 | AMR-150-0013 | Open Problems in Mathematical Logic — Problem 13 | Since every $F_\sigma$ set is Borel, Larman's theorem rules out the lowest
nontrivial possibility in the Borel hierarchy, but it does not settle the following problem.
Is there a Borel two-point set? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 13
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,002 | AMR-150-0014 | Open Problems in Mathematical Logic — Problem 14 | \begin{definition}
Let $F$ be a Borel field. A *Borel algebraically closed extension* of $F$ is a Borel field $K$, together with a Borel injective field homomorphism
\[
\iota:F\hookrightarrow K,
\]
such that $K$ is algebraically closed.
\end{definition}
[Montalb\'an--Nies {[MontalbanNies2013, Question 2.8]}]
Does ever... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 14
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,003 | AMR-150-0015 | Open Problems in Mathematical Logic — Problem 15 | However, for non-well-ordered cardinals, the situation deteriorates quickly. The sequel is the following.
For such a theory $T$, we want to show it is very close to a stongly minimal $T'$. It is like a vector space over fixed field or algebraically closed field. And since there is no well order, it is hard to take a ba... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 15
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,004 | AMR-150-0016 | Open Problems in Mathematical Logic — Problem 16 | In 1954, [Mar] shows that for $E\subseteq \mathbb{R}^2$ an analytic set with Hausdorff dimension 1. Then, for almost all $\theta$, the projection of $E$ onto a line with slope $\theta$ has Hausdorff dimension 1. Later in 1969, [Dav] shows that CH could imply there is some $E\subseteq \mathbb{R}^2$ with Hausdorff dimens... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 16
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
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"display_name": "AMR Open Problem Lists",
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,005 | AMR-150-0017 | Open Problems in Mathematical Logic — Problem 17 | Find more models $M$ and forcing notions $\mathbb{P}\in M$ such that $(*)$ is true. | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 17
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,006 | AMR-150-0018 | Open Problems in Mathematical Logic — Problem 18 | Suppose there are a model $M$ and a forcing notion $\mathbb{P}\in M$ such that $(*)$ is true. Can we deduce that $M\models [\exists\ \text{a large cardinal}]$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 18
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,007 | AMR-150-0019 | Open Problems in Mathematical Logic — Problem 19 | \quad If $\mathbf{a}<\mathbf{b}<\mathbf{c}$ are Turing degrees, and $\mathbf{a}$, $\mathbf{c}$ contain different Martin-L\"of randoms, then must $\mathbf{b}$ contain one? The answer is no.
Does this hold with a larger degree notion, for example, LR-degrees? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 19
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,008 | AMR-150-0020 | Open Problems in Mathematical Logic — Problem 20 | If $L_\beta\models\mbox{$\mathit{V}=\mathit{HC}$}$, then
\begin{align*}
\left(\mathcal{P}(\omega)\cap L_\beta\models\mathbf{s}ymbol{\Pi}_{m+1}^1\mathsf{-MI} \right)\iff\beta\mbox{ supports a strong }\Sigma_{m+1}\textrm{-nesting}.
\end{align*} | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 20
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,009 | AMR-150-0021 | Open Problems in Mathematical Logic — Problem 21 | Also note the following fact:
\begin{fact}
(1) There is a complete theory $T$ such that $=$ is Borel bi-reducible to $\cong\restriction_{\mathrm{Mod}(T)}$. For example, $T$ can be chosen as the theory of the equivalence relation on $\omega$ with infinitely many equivalence classes of any finite size.\\
(2) There is a c... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 21
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,010 | AMR-150-0022 | Open Problems in Mathematical Logic — Problem 22 | Maximal cofinitary groups have been studied by Bart Kastermans in [Kas]. It is known that maximal cofinitary groups cannot be $K_\sigma$, abelian, and there is a coanalytic maximal cofinitary group if assuming the axiom of constructibility. So we can ask similar questions for maximal finitely periodic groups:
Is there... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 22
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,011 | AMR-150-0023 | Open Problems in Mathematical Logic — Problem 23 | Natural questions about $A \mapsto I(A)$:
- Does the range of $I$ have the same cardinality as $2^{\mathbb{R}}$? (Seems yes under GCH.)
- If we consider the closed set $C$, $I(C)$ is arithmetic ($\mathbf{\Sigma}_2^0$). What's the complexity of the set
$$\big\{\mathbf{\Sigma}_2^0 \text{ formula } \varphi : \varphi \te... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 23
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,012 | AMR-150-0024 | Open Problems in Mathematical Logic — Problem 24 | Let $L_x=\{z : z \leq_K^+ x\}$ and $U_x=\{z : z \geq_K x\}$. Are the following true?
(1) $L_x$ is countable iff $\liminf_{n\to\infty}(K(x\upharpoonright n)-K(n))<\infty$;
(2) $U_x$ is countable iff $\liminf_{n\to\infty}(K(n)+n-K(x\upharpoonright n))<\infty$. | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 24
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,013 | AMR-150-0025 | Open Problems in Mathematical Logic — Problem 25 | Are the following true?
(1) For any c.e. set $A$, there exists a c.e. set $D\subseteq 2\mathbb{N}$, such that $A\equiv_{rK}D$ and $C(A\upharpoonright n|D\upharpoonright n)=C(D\upharpoonright n|A\upharpoonright n)=O(1)$;
(2) For all $x$, there is a random $z$ such that $z \geq_{rK} x$ (or $z \geq_K x$). | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 25
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "amr_open_problem_lists",
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,014 | AMR-150-0026 | Open Problems in Mathematical Logic — Problem 26 | It was shown in [Ba] that for $k=2,3$, Player 1 has a winning strategy in the game $G_k$. For $k\geq 4$, this is unknown.
For $k\geq 4$, does Player 1 have a winning strategy in the game $G_k$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 26
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,015 | AMR-150-0027 | Open Problems in Mathematical Logic — Problem 27 | Using recursion theory, Goh proved that any coanalytic separator of **WF** and **UB** is coanalytic complete. The method also proves Saint Raymond's theorem.
Can this be proved using Descriptive Set Theoretic methods? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 27
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
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"slug": "logic",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,016 | AMR-150-0028 | Open Problems in Mathematical Logic — Problem 28 (Downey--Hirschfeldt--Miller--Nies [DHMN]) | Is there an $x$ such that $\Omega^x \geq_T 0^{''}$ where
$$\Omega^x = \sum_{\sigma \in 2^{<\omega}} 2^{-K^x(\sigma)}$$
and
$$K^x(\sigma) = \min\{|\tau| : U^x(\tau) = \sigma\}?$$ | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 28
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Downey--Hirschfeldt--Miller--Nies [DHMN] | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,017 | AMR-150-0029 | Open Problems in Mathematical Logic — Problem 29 | - Is there a recursion theoretical proof for the above theorem of Velickovic--Woodin?
- Is the following true: For any $\Sigma_1^1(y)$ set $A$, if there is $x \in A$ such that $\omega_1^{CK(x)} > \omega_1^{CK(y)}$, then the Velickovic--Woodin theorem holds for $A$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 29
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,018 | AMR-150-0030 | Open Problems in Mathematical Logic — Problem 30 | $P^-$: For every positive tree there are distinct $(X_n : n \in \omega)$ such that $X_n \in [T]$.
\end{quote}
It is known that
$$\text{WKL}_0 \vdash P^+$$
and
$$\text{RCA}_0 \vdash P^+ \to P \to P^- \to \text{1-RAN} \leftrightarrow \text{WWKL}_0,$$
where $\text{1-RAN}$ means there exists a 1-random. But we also know th... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 30
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,019 | AMR-150-0031 | Open Problems in Mathematical Logic — Problem 31 | How about using dimension? (Define the above concepts by replacing measure by dimension.) | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 31
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,020 | AMR-150-0032 | Open Problems in Mathematical Logic — Problem 32 | It is known that
$$\text{I}\Sigma_n + \text{WPHP}(\Sigma_{n+1}) + \text{FRT}^e_k(\Sigma_{n+1})(e,k \text{ standard}) \nvdash \text{B}\Sigma_{n+1}$$
and
$$\text{FRT}^e_k(\Sigma_{n+1}) \nvdash \text{WPHP}(\Sigma_{n+1}).$$
The questions are:
$\text{I}\Sigma_{n+1} + \text{WPHP}(\Sigma_{n+1}) \vdash \text{FRT}_2^2(\Sigma_... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 32
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,021 | AMR-150-0033 | Open Problems in Mathematical Logic — Problem 33 | The first-order theory \text{2-RAN} is between $\text{CARD}(\Sigma_2)$ and $\text{WPHP}(\Sigma_2)$, but how about $\text{GPHP}(\Sigma_2)$ and \text{2-RAN}? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 33
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,022 | AMR-150-0034 | Open Problems in Mathematical Logic — Problem 34 | - Can such a group $L$ have unsolvable word problem?
- Is there a f.g., residually finite $\Pi$-group that is not effectively r.f.?
- Morozov (Higman’s question revisited, 2000) constructed a $\Pi$-group that is not isomorphic to a subgroup of $S_{\text{rec}}$. Can we make such a group r.f.? It can't be e.r.f. | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 34
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,023 | AMR-150-0035 | Open Problems in Mathematical Logic — Problem 35 | For each left $\Sigma_2$ real $r \in [0, 1]$ there is a computable profinite group and computable subgroup with Hausdorff dimension $r$.
Which values can occur for $r$ when $G$ is also topologically finitely generated? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 35
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,024 | AMR-150-0036 | Open Problems in Mathematical Logic — Problem 36 | Nies, Segal, and Tent 2021 [NST] studied expressiveness of f.o. logic for profinite group. Many such groups are axiomatised by single sentence in the language of groups, among this reference class.
For a f.o. sentence $\varphi$, what is the possible complexity of $\{G : G \models \varphi\}$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 36
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,025 | AMR-150-0037 | Open Problems in Mathematical Logic — Problem 37 | The following problem was also posed during the workshop, and by the end of the workshop Gao and Nies realized that the answer is yes.
Is there some Borel class of profinite groups with isomorphism relation properly between $S_\infty$-complete and smooth? In particular, how about the Abelian case? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 37
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,026 | AMR-150-0038 | Open Problems in Mathematical Logic — Problem 38 | Nies, Schlicht, and Tent proved in 2019 [NST2] that the topological isomorphism of oligomorphic groups is $\leq_B E_\infty$. Is it smooth? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 38
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,027 | AMR-150-0039 | Open Problems in Mathematical Logic — Problem 39 | If $G$ is oligomorphic, is $\text{Out}(G)$ always profinite? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 39
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,028 | AMR-150-0040 | Open Problems in Mathematical Logic — Problem 40 | Is there a Borel, invariant class $C$ of closed subgroups of $S_\infty$ with isomorphism relation not Borel below graph isomorphism? Analytic complete? How about the class $C$ of pro-countable groups? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 40
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
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801,029 | AMR-150-0041 | Open Problems in Mathematical Logic — Problem 41 | In [LMNS, Section 3.1] the authors showed the following implications
$$\text{1-generic } \Delta^0_2 \Rightarrow \text{ index guessable } \Rightarrow \text{ computes no maximal tower } \Rightarrow \text{ low }$$
In the above diagram, are the first and the second implications reversible? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 41
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,030 | AMR-150-0042 | Open Problems in Mathematical Logic — Problem 42 | Every degree of decidable categoricity is a degree of categoricity. Is the converse true?
A conjecture for this problem is that it is true for $d \geq 0^{(\alpha)}$, where $\alpha$ is 'sufficiently large' computable ordinal. Say, for $\alpha = \omega$. What happens with d.c.e. degrees $d$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 42
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
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"slug": "logic",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,031 | AMR-150-0043 | Open Problems in Mathematical Logic — Problem 43 | Ceer stands for computably enumerable equivalence relation on $\omega$. A diagonal function (or a fixed-point-free function) for a ceer $E$ is a total function $g(x)$ satisfying $\neg g(x) E x$ for all $x \in \omega$.
The following are three versions of this problem.
- Describe the class **Diag** containing those Tur... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 43
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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801,032 | AMR-150-0044 | Open Problems in Mathematical Logic — Problem 44 | Does every (effectively) compact left-c.e. Polish space have a computable (right c.e.) Polish copy? Related to this problem, Melnikov and Ng proved that there is a left c.e. Polish space with no computable Polish presentation. Similarly, Koh, Melnikov, and Ng proved that there is a left c.e. Polish space with no right ... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 44
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,033 | AMR-150-0045 | Open Problems in Mathematical Logic — Problem 45 | A computable Polish space $X$ is $\alpha$-categorical if for every pair of computable metric spaces $M$, $N$ such that $\bar{M} \cong \bar{N} \cong X$, there is
an $\alpha$-computable homeomorphism between $\bar{M}$ and $\bar{N}$. The least Turing degree $\alpha$ is the degree of (topological) categoricity of $X$.
$X$ ... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 45
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,034 | AMR-150-0046 | Open Problems in Mathematical Logic — Problem 46 | Is every/any c.e. degree the degree of topological categoricity? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 46
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,035 | AMR-150-0047 | Open Problems in Mathematical Logic — Problem 47 | \abstractbody{
Let $M$ be a model satisfying $\text{RCA}_0 + \text{B}\Sigma_n + \neg \text{I}\Sigma_n$. Fix a $\Pi_n$ subset $X$ of $M$ and assume $\langle A_s : s \in M \rangle$ is a sequence of pairwise disjoint $M$-finite sets such that $\forall s (A_s \cap X \neq \emptyset)$.
Is there a definable in $M$ choice fun... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 47
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,036 | AMR-150-0048 | Open Problems in Mathematical Logic — Problem 48 | Consider a tree $T$ which is $\Pi^0_1(\emptyset')$ in $M$. Assume there is a $g \in [T]$ such that $M[g] \models \text{B}\Sigma_2$. Is there a definable path $h \in [T]$ such that $M[h] \models \text{B}\Sigma_2$? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 48
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,037 | AMR-150-0049 | Open Problems in Mathematical Logic — Problem 49 | In 2021, Matt Foreman asked the following question:
Is the set $\{G \in 2^{\omega \times \omega} : G \text{ is a graph on } \omega \text{ and } G \cong G^c\}$ Borel? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 49
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,038 | AMR-150-0050 | Open Problems in Mathematical Logic — Problem 50 (The union problem) | If $E$ is a countable Borel equivalence relation and $E = \cup_n F_n$, where $F_n$ is hyperfinite and $F_n \subseteq F_{n+1}$ for each $n \in \omega$, is it true that $E$ is hyperfinite? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 50
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: The union problem | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,039 | AMR-150-0051 | Open Problems in Mathematical Logic — Problem 51 (The hf/hf problem) | Analogous to the above, we call a countable Borel equivalence relation *hyperfinite-over-hyperfinite* (or shortly, *hf/hf*) if there is a Borel partial order $\leq$ on $X$ such that
- if $x \leq y$, then $x E y$,
- the order type of $\leq \upharpoonright_{[x]}$ is a suborder of $\mathbb{Z}^2$.
If $E$ is hf/hf, is it... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 51
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: The hf/hf problem | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,040 | AMR-150-0052 | Open Problems in Mathematical Logic — Problem 52 | Inspired by the Frisch--Shinko--Vidnyánszky theorem, we ask:
Suppose there is a counterexample to the hf/hf problem. Is the set of all hyperfinite equivalence relations $\mathbf{\Sigma}_2^1$-complete? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 52
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "amr_open_problem_lists",
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,041 | AMR-150-0053 | Open Problems in Mathematical Logic — Problem 53 (Weiss' question) | Is the orbit equivalence relation of Borel action of countable amenable group hyperfinite? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 53
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Weiss' question | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,042 | AMR-150-0054 | Open Problems in Mathematical Logic — Problem 54 | Also the connected equivalence relations of the following graphs are proved to be hyperfinite:
\begin{quote}
Graphs of polynomial growth (Bernshteyn--Yu),
Graph of growth less than $\exp(r^c)$ for some small enough $0<c<1$ (Grebík--Marks--Rozhoň--Shinko).
\end{quote}
How about graphs of uniform subexponential growth,... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 54
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,043 | AMR-150-0055 | Open Problems in Mathematical Logic — Problem 55 | For $x\in \text{Act}(F_\infty, ([0,1],\lambda))$, let $\mbox{Sch}(x)$ denote the Schreier graph of the action on $[0,1]$.
Is the set
$$\{x \in \text{Act}(F_\infty,([0,1],\lambda)) : \text{Sch}(x) \text{ has a measurable perfect matching}\}$$
$\mathbf{\Sigma}_1^1$-complete? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 55
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,044 | AMR-150-0056 | Open Problems in Mathematical Logic — Problem 56 (Halmos, 1956) | What $T \in \text{Aut}([0,1],\lambda)$ has $S \in \text{Aut}([0,1],\lambda)$ with $T = S^2 = S \circ S$?
Conjecture: $\{T \in \text{Aut}([0,1],\lambda) : \exists S \in \text{Aut}([0,1],\lambda) T = S^2\}$ is $\mathbf{\Sigma}_1^1$-complete. | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 56
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Halmos, 1956 | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,045 | AMR-150-0057 | Open Problems in Mathematical Logic — Problem 57 | If $\vec{G}$ is a Borel locally finite directed graph whose in-degrees are uniformly bounded and out-neighborhoods have polynomial growth, is the connected equivalence relation of $\vec{G}$ hyperfinite? | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 57
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,046 | AMR-150-0058 | Open Problems in Mathematical Logic — Problem 58 | Let $\alpha$ be a free, probability measure preserving (p.m.p.) and ergodic action of $\mathbb{F}_2$ on measure space $(X,\mu)$.
- If $e \neq x \in \mathbb{F}_2$, is there a free, p.m.p action $\beta$ such that $E_\alpha = E_\beta$ and $x$ acts ergodically?
- (Miller--Tserunyan). Is there a free, p.m.p action $\beta$... | Source list: Barmpalias, Gao et al. - Open Problems in Mathematical Logic (2026)
Source item: Problem 58
Source URL: https://arxiv.org/abs/2608.26628
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Barmpalias, Gao et al. | 2,026 | 18 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,047 | AMR-151-0001 | Open Problems for Painleve Equations — Problem 1 | \quad
\itemsep=0pt
- The Runge--Kutta method, and variants, are standard ODE solvers. Can we do better for integrable equations such as the Painlev\'e equations?
- Painlev\'e equations are ``integrable" and solvable by the isomonodromy method through an associated Riemann--Hilbert problem. How can we use this in the... | Source list: Clarkson - Open Problems for Painleve Equations (2019)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1901.10122
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Clarkson | 2,019 | 9 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,048 | AMR-151-0002 | Open Problems for Painleve Equations — Problem 2 | The Painlev\'e equations are known to have a cornucopia of properties such as: a Hamiltonian representation; exact solutions (rational solutions, algebraic solutions, solutions in terms of classical special solutions);
B\"acklund transformations (which relate two solutions of a Painlev\'e equation); associated isomonod... | Source list: Clarkson - Open Problems for Painleve Equations (2019)
Source item: Problem 2
Source URL: https://arxiv.org/abs/1901.10122
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Clarkson | 2,019 | 9 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,049 | AMR-152-0001 | Henon Maps: Open Problems — Question 1 | Can we find a H\'enon map (of some degree) which admits
a wild attractor, i.e., a Cantor set which attracts a set of Lebesgue positive measure and which is strictly included in a transitive set ? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 1
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,050 | AMR-152-0002 | Henon Maps: Open Problems — Question 2 | Returning to stochastic attractors, observe that
the existence of a parameter $c\in \mathbb{R}$ for which the quadratic map $x \mapsto x^2+c$
displays an absolutely continuous measure is easy to ensure. It suffices to pick
a parameter $c$ such that the post-critical orbit is finite but not periodic.
In dimension $2$, t... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 2
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,051 | AMR-152-0003 | Henon Maps: Open Problems — Question 3 | Do there exist $\varepsilon>0$ and a locally dense set (i.e., whose closure has non-empty interior.) $E$ of quadratic H\'enon maps for which
every point starting in some set of Lebesgue measure at least $\varepsilon$ has non-statistical behavior? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 3
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,052 | AMR-152-0004 | Henon Maps: Open Problems — Question 4 | It is natural to ask whether the third condition is superfluous. The recent result [OC23] suggests that this may be the case.
Is there a real, conservative, polynomial H\'enon map with an annular rotation domain?
Is there an open set of such real, conservative, polynomial H\'enon maps? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 4
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,053 | AMR-152-0005 | Henon Maps: Open Problems — Question 5 | An annular rotation domain is said to be trivial when the whole dynamics is conjugate to a rotation.
Is there an entire (i.e., an analytic map which extends to a holomorphic map of $\mathbb{C}^2$.) symplectomorphism of $\mathbb{R}^2$ with a non trivial annular rotation domain? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 5
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,054 | AMR-152-0006 | Henon Maps: Open Problems — Question 6 | Under this assumption, and in restriction to any open topological disc $D\subset \mathbb{R}^2$ that is compactly mapped inside itself, the dynamics is semi-conjugated to a (non-trivial) continuous map of a real tree. Other strong consequences can be derived (e.g., a closing lemma, or a description of zero entropy dynam... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 6
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,055 | AMR-152-0007 | Henon Maps: Open Problems — Question 7 | When $|b|$ is larger but smaller than $1/4$ (so that it is mildly dissipative),
[CPT] describes the dynamics of $f_{c,b}\in \mathcal{E}_0$.
In particular, all maps $f_{c,b}\in \partial \mathcal{E}_0$ are infinitely renormalizable (with renormalization periods eventually equal to $2$), solving a conjecture by Tresser (w... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 7
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,056 | AMR-152-0008 | Henon Maps: Open Problems — Question 8 | It is also natural to try to describe the boundary $\partial\mathcal{E}_0$: is it a (piecewise smooth) arc?
One would like to implement the strategy developed in [dCLM] for $b$ close to $0$:
Let us consider any infinitely renormalizable mildly dissipative map in $\mathcal{E}_0$.
Does the sequence of renormalizations c... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 8
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,057 | AMR-152-0009 | Henon Maps: Open Problems — Question 9 | We also don't know if different combinatorics of the renormalizations may occur.
Does there exist a mildly dissipative map $f_{c,b}\in \mathcal{E}_0$
which admits arbitrarily deep renormalizations with odd periods? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 9
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,058 | AMR-152-0010 | Henon Maps: Open Problems — Question 10 | As mentioned previously, for mildly dissipative real H\'enon maps the set of periodic points is dense
in the union of the supports of the invariant probability measures [CP].
The same property holds for any complex H\'enon maps [MR4142445].
For any real H\'enon map, does the closure of the set of periodic orbits suppo... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 10
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,059 | AMR-152-0011 | Henon Maps: Open Problems — Question 11 | For any map $f_{c,b}$ and any infinite set of periodic saddles $(p_n)$
which are pairwise not homoclinically related, do we have
$\min(|\lambda^-(p_n)|,|\lambda^+(p_n)|)\underset{n\to \infty}\longrightarrow 0$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 11
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,060 | AMR-152-0012 | Henon Maps: Open Problems — Problem 12 | Very recently, in [BSt], the authors developed a kneading theory for the H\'enon maps $H_{a,b}$ within a set of parameters $\mathcal{WY}$
for which Wang and Young proved the existence of a strange attractor.
This set has positive measure and consist of maps which are strongly dissipative.
We refer to [BSt] and [WY] for... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Problem 12
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,061 | AMR-152-0013 | Henon Maps: Open Problems — Question 13 | Is it true that any two distinct kneading sequences of the H\'enon map $H_{a,b}$, with $(a,b) \in \mathcal{WY}$, determine a unique pair of parameters $(a,b)$, and in that way govern all the other kneading sequences in $\mathfrak{K}$ of $H_{a,b}$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 13
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,062 | AMR-152-0014 | Henon Maps: Open Problems — Question 14 | We say that $H_2$ has small cycles if for any neighborhood $U$ of the origin $\mathbf{s}ymbol{0}$ in $\mathbb{C}^2$, there exists a cycle of $H_2$ which is entirely contained in $U\smallsetminus \{\mathbf{s}ymbol{0}\}$.
Does $H_2$ have small cycles? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 14
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,063 | AMR-152-0015 | Henon Maps: Open Problems — Question 15 | Does $H_2$ have both small saddle cycles and small elliptic cycles? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 15
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,064 | AMR-152-0016 | Henon Maps: Open Problems — Question 16 | We say that $H_2$ has a Herman ring with rotation number $\theta\in (\mathbb{R}\smallsetminus \mathbb{Q})/\mathbb{Z}$ if there exists an annulus $V= \bigl\{z\in \mathbb{C}/\mathbb{Z} : \mathrm{Im}(z)<h\bigr\}$ with $h>0$, a holomorphic map $\phi\colon V\to \mathbb{C}^2$, and an integer $n\geq 2$ such that
\[\forall z\i... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 16
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,065 | AMR-152-0017 | Henon Maps: Open Problems — Question 17 | If the answer is yes, we may consider the set $\Theta\subset (\mathbb{R}-\mathbb{Q})/\mathbb{Z}$ of rotation numbers $\theta$ such that $H_2$ has a Herman ring with rotation number $\theta$.
Does $\Theta$ have positive Lebesgue measure? More precisely, is $0$ a Lebesgue density point of $\Theta$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 17
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,066 | AMR-152-0018 | Henon Maps: Open Problems — Question 18 | Assume $H_2$ has a Herman ring with bounded type rotation number $\theta$. Is it possible to find parameters $a\in \mathbb{D}\smallsetminus \{0\}$ arbitrarily close to $1$ such that the dissipative H\'enon map $H\colon\mathbb{C}^2\to \mathbb{C}^2$ defined by
\[H(x,y) = \left(ay,x+y^2\right).\]
has a Herman ring with ro... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 18
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,067 | AMR-152-0019 | Henon Maps: Open Problems — Question 19 | Recall the following standard definitions (see [BS]). Let $K^\pm$ denote the set of points with bounded forward orbits for $f^\pm$. We denote $J^\pm:= \partial K^\pm$. We also define $J:= J^+ \cap J^-$ and $J^*$ to be the closure of ${\mathcal{S}}$ (hence $J^* \subset J$).
If $f$ is quasi-hyperbolic, then is $\mathrm{... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 19
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,068 | AMR-152-0020 | Henon Maps: Open Problems — Question 20 | If $f$ is quasi-hyperbolic, then is there no wandering Fatou component? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 20
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,069 | AMR-152-0021 | Henon Maps: Open Problems — Question 21 | If $f$ is quasi-hyperbolic, do the unstable slices satisfy a John-type condition (as in [BS7])? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 21
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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