Linear algebraic groups and countable Borel equivalence relations

DOI10.1090/S0894-0347-00-00341-6zbMath0952.03057MaRDI QIDQ4501059

Scot Adams, Alexander S. Kechris

Publication date: 3 September 2000

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

cocyclesBorel equivalence relationsBorel reducibilitysuperrigidity

Mathematics Subject Classification ID

Descriptive set theory (03E15) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

Related Items (37)

The classification problem for torsion-free abelian groups of finite rank ⋮ THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF RANK TWO ⋮ Borel cardinalities below $c_0$ ⋮ Completeness of the isomorphism problem for separable \(C^\ast\)-algebras ⋮ COUNTABLE BOREL EQUIVALENCE RELATIONS ⋮ Borel equivalence relations and cardinal algebras ⋮ Complete analytic equivalence relations ⋮ Can we classify complete metric spaces up to isometry? ⋮ Souslin quasi-orders and bi-embeddability of uncountable structures ⋮ PROPERTY τ AND COUNTABLE BOREL EQUIVALENCE RELATIONS ⋮ The classification problem for \(S\)-local torsion-free abelian groups of finite rank ⋮ Rotation equivalence and cocycle superrigidity ⋮ Every CBER is smooth below the Carlson–Simpson generic partition ⋮ Low-dimensional solenoidal manifolds ⋮ Borel structures on the space of left‐orderings ⋮ Anti-classification results for groups acting freely on the line ⋮ Borel reductions of profinite actions of SL\(_n(\mathbb Z)\) ⋮ Complexity of Ramsey null sets ⋮ Uniform Martin’s conjecture, locally ⋮ The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism ⋮ Well-Quasi Orders and Hierarchy Theory ⋮ A complexity problem for Borel graphs ⋮ Orthogonal measures and ergodicity ⋮ Infinite-Time Turing Machines and Borel Reducibility ⋮ Some applications of the Adams-Kechris technique ⋮ On the Complexity of the Classification Problem for Torsion-Free Abelian Groups of Finite Rank ⋮ Classifying Borel automorphisms ⋮ The smooth ideal ⋮ Generalized Descriptive Set Theory and Classification Theory ⋮ Popa superrigidity and countable Borel equivalence relations ⋮ On the complexity of Borel equivalence relations with some countability property ⋮ On the complexity of the classification problem for torsion-free abelian groups of rank two. ⋮ Borel complexity of isomorphism between quotient Boolean algebras ⋮ A cofinal family of equivalence relations and Borel ideals generating them ⋮ Superrigidity and countable Borel equivalence relations ⋮ Uniformity, universality, and computability theory ⋮ Orienting Borel graphs

Cites Work

• Indecomposability of treed equivalence relations
• Descriptive set theory
• Groups generating transversals to semisimple Lie group actions
• Transformation groups and \(C^ *\)-algebras
• A Borel reductibility theory for classes of countable structures
• Counting the number of equivalence classes of Borel and coanalytic equivalence relations
• Trees and amenable equivalence relations
• A Glimm-Effros Dichotomy for Borel Equivalence Relations
• Countable sections for locally compact group actions
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
• New Directions in Descriptive Set Theory
• A Note on Borel Equivalence Relations
• The Structure of Hyperfinite Borel Equivalence Relations
• COUNTABLE BOREL EQUIVALENCE RELATIONS
• Groups of Automorphisms of Borel Spaces
• Locally Compact Transformation Groups
• Borel equivalence relations and classifications of countable models
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