A Converse to Dye’s Theorem

  title={A Converse to Dye’s Theorem},
  author={Greg Hjorth},
Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F2 on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not universal for treeable in the ≤B ordering. 
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