Date:
Wed, 13/10/202114:00-16:00
Title:
Structurability of Countable Borel Equivalence Relations
Abstract:
Chen and Kechris defined when a countable Borel equivalence relation (CBER) E on a standard Polish space X is structurable by a countable relational model M: The relations must define Borel subsets of a power of X, and the restriction to each E-class must give a model isomorphic to M. The structurability of E by various models can shed light on its properties as a CBER. One interesting question is, Which models structure every CBER? I'll discuss an adaptation by Marks of a construction of Ackerman, Freer, and Patel which finds a large class of such models. I'll also show some applications of their construction to this question. Time permitting I'll discuss some related results and techniques from my thesis.
Structurability of Countable Borel Equivalence Relations
Abstract:
Chen and Kechris defined when a countable Borel equivalence relation (CBER) E on a standard Polish space X is structurable by a countable relational model M: The relations must define Borel subsets of a power of X, and the restriction to each E-class must give a model isomorphic to M. The structurability of E by various models can shed light on its properties as a CBER. One interesting question is, Which models structure every CBER? I'll discuss an adaptation by Marks of a construction of Ackerman, Freer, and Patel which finds a large class of such models. I'll also show some applications of their construction to this question. Time permitting I'll discuss some related results and techniques from my thesis.