Some Applications of the Adams-Kechris Technique
colorful horizontal rule

Su Gao

Abstract

We analyze the technique used by Adams and Kechris in [1] to obtain their results about Borel reducibility of countable Borel equivalence relations. Using this technique, we show that every analytic equivalence relation is Borel reducible to the Borel bi-reducibility of countable Borel equivalence relations. We also apply the technique to two other classes of non-essentially countable Borel equivalence relations and derive analogous results for the classificiation problem of Borel automorphisms.

[1] S. Adams and A. S. Kechris, Linear algebraic groups and countable Borel equivalence relations, preprint, 1999.

Table of Contents

  1. Introduction
  2. Elements of the Technique
  3. Non-Essentially Countable Equivalence Relations
  4. Another Class of Borel Equivalence Relations
  5. Borel Automorphisms and Further Questions
    References

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