Superrigidity and countable Borel equivalence relations

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Abstract

We formulate a Borel version of a corollary of Furman's superrigidity theorem for orbit equivalence and present a number of applications to the theory of countable Borel equivalence relations. In particular, we prove that the orbit equivalence relations arising from the natural actions of SL3(ℤ) on the projective planes over the various p-adic fields are pairwise incomparable with respect to Borel reducibility.

Original languageEnglish (US)
Pages (from-to)237-262
Number of pages26
JournalAnnals of Pure and Applied Logic
Volume120
Issue number1-3
DOIs
StatePublished - Apr 15 2003

All Science Journal Classification (ASJC) codes

  • Logic

Keywords

  • Borel equivalence relation
  • Superrigidity

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