Stable decompositions and rigidity for products of countable equivalence relations

Countable Borel Equivalence Relations

This paper is a contribution to a new direction in descriptive set theory that is being extensively pursued over the last decade or so. It deals with the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This study is motivated by basic foundational questions,...

Rigidity theorems for actions of product groups and countable Borel equivalence relations

Popa Superrigidity and countable Borel equivalence relations

We present some applications of Popa’s Superrigidity Theorem to the theory of countable Borel equivalence relations. In particular, we show that the universal countable Borel equivalence relation E∞ is not essentially free.

Recursion Theory and Countable Borel Equivalence Relations

Recursion theory and countable Borel equivalence relations

Forcing Constructions and Countable Borel Equivalence Relations

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply the nonexistence of Borel complete sections with certain