On the complexity of the classification problem for torsion-free abelian groups of rank two.

DOI10.1007/BF02392844zbMath1038.20042MaRDI QIDQ1812471

Simon Thomas

Publication date: 11 September 2003

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

Borel probability measurestandard Borel spaceHjorth-Kechris conjecturerigid torsion-free abelian groupsVitali equivalence relation

Mathematics Subject Classification ID

Other classical set theory (including functions, relations, and set algebra) (03E20) Torsion-free groups, finite rank (20K15) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (11)

The classification problem for torsion-free abelian groups of finite rank ⋮ THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF RANK TWO ⋮ Completeness of the isomorphism problem for separable \(C^\ast\)-algebras ⋮ Rotation equivalence and cocycle superrigidity ⋮ Low-dimensional solenoidal manifolds ⋮ Anti-classification results for groups acting freely on the line ⋮ Borel reductions of profinite actions of SL\(_n(\mathbb Z)\) ⋮ Classifying singularities up to analytic extensions of scalars is smooth ⋮ Measuring the classification difficulty of countable torsion-free Abelian groups. ⋮ Popa superrigidity and countable Borel equivalence relations ⋮ Superrigidity and countable Borel equivalence relations

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