Borel graphable equivalence relations

Authors: Arant, Tyler ^a, Kechris, Alexander S. ^{b, 1}, Lutz, Patrick ^{c, ⁎, 2}

Source: In Advances in Mathematics March 2026 487

Borel complexity of sets of points with prescribed Birkhoff averages in Polish dynamical systems with a specification property

Authors: KONRAD DEKA, STEVE JACKSON, DOMINIK KWIETNIAK, BILL MANCE

Source: Ergodic Theory and Dynamical Systems. 45:2695-2723

Subject Terms: Logic, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), specification property, Symbolic dynamics, generic points, Dynamical Systems (math.DS), 01 natural sciences, Dynamical Systems, Borel hierarchy, FOS: Mathematics, Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems, 0101 mathematics, Logic (math.LO), Descriptive set theory

File Description: application/xml

Access URL: http://arxiv.org/abs/2210.08937
https://ruj.uj.edu.pl/handle/item/559348

Guarded Fraïssé Banach spaces

Authors: Cúth, Marek ^a, de Rancourt, Noé ^{c, ⁎}, Doucha, Michal ^b

Source: In Advances in Mathematics October 2026 502 Part C

Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs: Generating sets and algebraic properties of pure mapping class groups of infinite graphs

Authors: Domat, George, Hoganson, Hannah, Kwak, Sanghoon

Source: Annales Henri Lebesgue. 8:373-416

Subject Terms: Topological methods in group theory, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Topological properties of groups of homeomorphisms or diffeomorphisms, Geometric Topology (math.GT), Group Theory (math.GR), mapping class groups, 57S05, 37E25, 57M07, 20E08, 20F65, 54H05, proper homotopy equivalence, Group Theory, Geometric Topology, Dynamical systems involving maps of trees and graphs, FOS: Mathematics, Groups acting on trees, \(\mathrm{Out}(F_n)\), coarse geometry, Geometric group theory

File Description: application/xml

Access URL: http://arxiv.org/abs/2309.07885

The uniform Gardner conjecture and rounding Borel flows

Authors: Bowen, Matthew, Kun, Gábor, Sabok, Marcin

Source: Proceedings of the American Mathematical Society. 153:3607-3618

Subject Terms: Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, Mathematics - Logic, Dynamical Systems (math.DS), 01 natural sciences, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Dissections and valuations (Hilbert's third problem, etc.), Mathematics - Dynamical Systems, 0101 mathematics, Flows in graphs, Logic (math.LO), Descriptive set theory, 03E15, 05C21, 37A20, 52B45

File Description: application/xml

Access URL: http://arxiv.org/abs/2212.03785

Analogues of the countable Borel equivalence relations in the setting of computable reducibility

Authors: Andrews, Uri, San Mauro, Luca

Source: Proceedings of the American Mathematical Society. 153:3577-3593

Subject Terms: FOS: Mathematics, Other degrees and reducibilities in computability and recursion theory, Mathematics - Logic, 03D30, 03E15, Logic (math.LO), Descriptive set theory, Hierarchies of computability and definability

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Access URL: http://arxiv.org/abs/2409.17018

Borel complexity of the isomorphism relation of Archimedean orders in finitely generated groups

Authors: Poulin, Antoine

Source: Proceedings of the American Mathematical Society. 153:3595-3605

Subject Terms: General groups of measure-preserving transformations and dynamical systems, FOS: Mathematics, Ordered groups, Mathematics - Logic, Dynamical Systems (math.DS), Group Theory (math.GR), Mathematics - Dynamical Systems, Logic (math.LO), Descriptive set theory, Mathematics - Group Theory

File Description: application/xml

Access URL: http://arxiv.org/abs/2403.11326

The Borel complexity of the class of models of first-order theories

Authors: Andrews, Uri, Gonzalez, David, Lempp, Steffen, Rossegger, Dino, Zhu, Hongyu

Source: Proceedings of the American Mathematical Society. 153(09)

Subject Terms: Pure Mathematics, Mathematical Sciences, Models of arithmetic, Borel complexity, countable models, descriptive set theory, Pure mathematics

File Description: application/pdf

Access URL: https://escholarship.org/uc/item/87t7x2jk
https://escholarship.org/content/qt87t7x2jk/qt87t7x2jk.pdf

THE WEIHRAUCH LATTICE AT THE LEVEL OF $\boldsymbol {\Pi }^1_1{-}\mathsf{CA}_0$ : THE CANTOR–BENDIXSON THEOREM: The Weihrauch lattice at the level of \(\boldsymbol{\Pi }^1_1{-}\mathsf{CA}_0\): the Cantor-Bendixson theorem

Authors: Vittorio Cipriani, Alberto Marcone, Manlio Valenti

Source: The Journal of Symbolic Logic. 90:752-790

Subject Terms: computable analysis, Weihrauch degrees, Logic, perfect sets, Cantor-Bendixson theorem, Foundations of classical theories (including reverse mathematics), 01 natural sciences, descriptive set theory, FOS: Mathematics, Other degrees and reducibilities in computability and recursion theory, reverse mathematics, 0101 mathematics, Computation over the reals, computable analysis, Logic (math.LO), Descriptive set theory, 03D78 (Primary) 03E15, 03B30, 03D30 (Secondary)

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Access URL: http://arxiv.org/abs/2210.15556

On small analytic relations

Authors: Lecomte, Dominique

Contributors: Vilbert, Martine

Source: Fundamenta Mathematicae. 269:1-44

Subject Terms: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), [MATH] Mathematics [math], countable, Borel class, 01 natural sciences, Graph, Descriptive complexity, antichain basis, analytic relation, FOS: Mathematics, 0101 mathematics, Countable, Mathematics - General Topology, continuous reducibility, acyclic, General Topology (math.GN), Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Mathematics - Logic, graph, A cyclic, Antichain basis, descriptive complexity, Analytic relation, Continuous reducibility, Ramsey, Logic (math.LO), Descriptive set theory

File Description: application/xml

Access URL: http://arxiv.org/abs/2005.13212
https://zbmath.org/8036572
https://doi.org/10.4064/fm200603-26-1
https://hal.science/hal-05066966v1
https://doi.org/10.4064/fm200603-26-1

Technical Supplement and Formal Resolution of the Analytic P vs NP Problem (Exposition of ZFC-Based Proofs)

Authors: Sahbani, Abdellatif

Subject Terms: Axiom of Bounded Computation, Descriptive Set Theory, Constructible Universe (L), PvsNP, ZFC Independence, Landauer's Principle

Proximal motion planning algorithms

Authors: Melih İs, İsmet Karaca

Contributors: Repositorio Institucional de la Universitat Politècnica de València Riunet, Ege University Institutional Repository

Source: RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Universitat Politècnica de València (UPV)
Applied General Topology, Vol 26, Iss 1, Pp 131-162 (2025)

Subject Terms: QA299.6-433, nearness theory, Discriminantal varieties and configuration spaces in algebraic topology, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Proximity, Descriptive Proximity, Motion Planning, Nearness Theory, Topological Complexity, Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects), proximity, 54E17, 55M30, 54H05, 55R80, Nearness spaces, motion planning, QA1-939, FOS: Mathematics, Algebraic Topology (math.AT), topological complexity, Mathematics - Algebraic Topology, Mathematics, Analysis, descriptive proximity

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/abs/2305.13726
https://riunet.upv.es/handle/10251/221866
https://zbmath.org/8068215
https://doi.org/10.4995/agt.2025.21183
https://doaj.org/article/02d21c5c4e4741b2ae11ec5acd25471d
https://hdl.handle.net/11454/119253
https://hdl.handle.net/11454/121698
https://doi.org/10.4995/agt.2025.21183

ON SOME OF BROUWER’S AXIOMS: On some of Brouwer's axioms

Authors: Wim Veldman

Source: The Bulletin of Symbolic Logic, 31, 1, pp. 1-52

Subject Terms: Algebra and Topology, continuity principle, fan theorem, bar theorem, intuitionistic mathematics, Borel hierarchy theorem, Mathematics - Logic, 06 humanities and the arts, almost-fan theorem, Intuitionistic mathematics, 0603 philosophy, ethics and religion, 01 natural sciences, 03F55, constructive measure theory, Ramsey's theorem, FOS: Mathematics, Algebra en Topologie, 0101 mathematics, Logic (math.LO), Descriptive set theory, Mathematics, Constructive and recursive analysis

File Description: application/xml

Access URL: http://arxiv.org/abs/2202.06078
https://zbmath.org/8030894
https://doi.org/10.1017/bsl.2024.52
https://hdl.handle.net/2066/319128

On algebraic sums, trees and ideals in the Baire space

Authors: Lukasz Mazurkiewicz, Marcin Michalski, Robert Ralowski, Szymon Zeberski

Source: Archive for Mathematical Logic. 64:843-855

Subject Terms: perfect set, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), General Topology (math.GN), ideal, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Baire space, Cardinal characteristics of the continuum, perfect tree, FOS: Mathematics, Applications of set theory, Miller tree, Primary: 03E75, 28A05, 54H05, Secondary: 03E17, algebraic sum, Mathematics - General Topology

File Description: application/xml

Access URL: http://arxiv.org/abs/2409.17748
https://zbmath.org/8068337
https://doi.org/10.1007/s00153-025-00966-5

Convex embeddability and knot theory

Authors: Martina Iannella, Alberto Marcone, Luca Motto Ros, Vadim Weinstein

Source: Transactions of the American Mathematical Society. 378:2745-2796

Subject Terms: Mathematics - Geometric Topology, FOS: Mathematics, Knot theory, Mathematics - Combinatorics, Geometric Topology (math.GT), Mathematics - Logic, Combinatorics (math.CO), Total orders, Logic (math.LO), Descriptive set theory, Wild embeddings, 03E15, 06A05, 57K10, 57M30

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2309.09910
https://zbmath.org/8013999
https://doi.org/10.1090/tran/9334
https://arxiv.org/abs/2309.09910
https://hdl.handle.net/2318/2033130
https://doi.org/10.1090/tran/9334

Scott analysis, linear orders, and almost periodic functions

Authors: David Gonzalez, Matthew Harrison‐Trainor, Meng‐Che 'Turbo' Ho

Source: Bulletin of the London Mathematical Society. 57:1118-1139

Subject Terms: FOS: Mathematics, Computable structure theory, computable model theory, Mathematics - Logic, Total orders, Logic (math.LO), Descriptive set theory, Theory of numerations, effectively presented structures

File Description: application/xml

Access URL: http://arxiv.org/abs/2406.01836

A note on a theorem of Hausdorff

Authors: Pol, Roman, Reńska, Mirosława

Source: Proceedings of the American Mathematical Society. 152:4915-4921

Subject Terms: countable-dimensional, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), \(G_\delta\)-set, Hausdorff gap, zero-dimensional, Compact (locally compact) metric spaces, Descriptive set theory, ccc \(\sigma\)-ideals, Dimension theory in general topology

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Maximal sets without choice

Authors: Schilhan, Jonathan

Source: In Annals of Pure and Applied Logic April 2026 177(4)

Forcing Axioms and Generic Absoluteness for Projective Sets in Descriptive Set Theory

Authors: Revista, Zen, MFC, 10

Subject Terms: Universally Baire Sets, Proper Forcing Axiom, Generic Absoluteness, Descriptive Set Theory, Projective Hierarchy, Stationary Tower, Woodin Cardinals, Large Cardinals

Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups

Authors: Petr Naryshkin, Andrea Vaccaro

Source: Math Ann

Subject Terms: Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, Mathematics - Logic, Group Theory (math.GR), Dynamical Systems (math.DS), Article, measurable action, Gromov boundary, Hyperbolic groups and nonpositively curved groups, Borel space, Borel action of countable group, FOS: Mathematics, geodesic ray bundle, Mathematics - Dynamical Systems, Logic (math.LO), Geometric group theory, Descriptive set theory, Mathematics - Group Theory, Borel equivalence relation

File Description: application/xml

Access URL: https://pubmed.ncbi.nlm.nih.gov/40191169
http://arxiv.org/abs/2306.02056