Anti-classification results for groups acting freely on the line
DOI10.1016/j.aim.2023.108938OpenAlexW3092670483MaRDI QIDQ2692557
Assaf Shani, Filippo Calderoni, Luca Motto Ros, David Marker
Publication date: 22 March 2023
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.08049
Borel equivalence relationso-minimalityBorel reducibilityArchimedean ordered groupschoiceless modelscircularly ordered groups
Descriptive set theory (03E15) Applications of set theory (03E75) Axiomatics of classical set theory and its fragments (03E30) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Ordered groups (06F15) Ordered groups (group-theoretic aspects) (20F60) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Model theory of ordered structures; o-minimality (03C64) Model theory of denumerable and separable structures (03C15)
Cites Work
- Completeness of the isomorphism problem for separable \(C^\ast\)-algebras
- Left-orderings on free products of groups
- On the dynamics of (left) orderable groups.
- The conjugacy problem in ergodic theory
- Free lattice-ordered groups and the space of left orderings
- The isomorphism problem for torsion-free abelian groups is analytic complete
- Borel equivalence relations induced by actions of the symmetric group
- Laminations and groups of homeomorphisms of the circle
- Groups acting on the circle.
- On the number of circular orders on a group
- Spaces of invariant circular orders of groups
- On isometry and isometric embeddability between ultrametric Polish spaces
- On the complexity of the classification problem for torsion-free abelian groups of rank two.
- An anti-classification theorem for ergodic measure preserving transformations
- Promoting circular-orderability to left-orderability
- Left-orderable groups that don't act on the line
- Transformation groups and \(C^ *\)-algebras
- On Fraissé's order type conjecture
- Models of ZF-set theory
- A Borel reductibility theory for classes of countable structures
- The space of left orders of a group is either finite or uncountable
- Ordered groups and topology
- Models of ZF with the same sets of sets of ordinals
- Cohen and Set Theory
- Counting the number of equivalence classes of Borel and coanalytic equivalence relations
- Vaught's conjecture for o-minimal theories
- A Glimm-Effros Dichotomy for Borel Equivalence Relations
- New Directions in Descriptive Set Theory
- Linear algebraic groups and countable Borel equivalence relations
- COUNTABLE BOREL EQUIVALENCE RELATIONS
- The Bristol model: An abyss called a Cohen real
- Group orderings, dynamics, and rigidity
- ITERATING SYMMETRIC EXTENSIONS
- What is ... a Borel reduction?
- The classification problem for torsion-free abelian groups of finite rank
- Set Theory
- The isomorphism relation on countable torsion free abelian groups
- TOPOLOGY ON THE SPACES OF ORDERINGS OF GROUPS
- THE BOREL COMPLEXITY OF ISOMORPHISM FOR O-MINIMAL THEORIES
- CLASSES OF BARREN EXTENSIONS
- Borel reducibility and symmetric models
- Free products of circularly ordered groups with amalgamated subgroup
- The complexity of continuous embeddability between dendrites
- Complete analytic equivalence relations
- Cofinal families of Borel equivalence relations and quasiorders
- The classification of hypersmooth Borel equivalence relations
- Locally Compact Transformation Groups
- Independent sets in topological algebras
- The axiom of choice
- Borel structures on the space of left‐orderings
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