Marcin Sabok : Canonization of Borel equivalence relations

Posted by Lynn Scow , part of the Logic Seminar.

At

Oct. 9, 2012, 4 p.m.

In

SEO 427

Abstract

I will discuss some recent developments in canonical Ramsey theory in the context of descriptive set theory. I will survey canonization results for various classes of equivalence relations. I will show that hypersmooth equivalence relations canonize to three equivalences: two trivial ones and $E_1$. I will also show that equivalence relations reducible to $E_2$ also canonize to three equivalences: the two trivial ones and $E_2$. This is part of a joint forthcoming book with Vladimir Kanovei and Jindra Zapletal.