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Article
Borel Reductions of Profinite Actions of SLn(ℤ)
Annals of Pure and Applied Logic (2010)
  • Samuel Coskey, City University of New York
Abstract
Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank strictly increases in complexity with the rank. Subsequently, Thomas proved that the complexities of the classification problems for p-local torsion-free abelian groups of fixed rank n are pairwise incomparable as p varies. We prove that if 3≤m<n and p,q are distinct primes, then the complexity of the classification problem for p-local torsion-free abelian groups of rank m is again incomparable with that for q-local torsion-free abelian groups of rank n.
Keywords
  • Countable Borel equivalence relations,
  • Torsion-free abelian groups,
  • Superrigidity
Disciplines
Publication Date
July 1, 2010
Citation Information
Samuel Coskey. "Borel Reductions of Profinite Actions of SLn(ℤ)" Annals of Pure and Applied Logic Vol. 161 (2010)
Available at: http://works.bepress.com/samuel_coskey/3/