Canonization of Borel equivalence relations

**Abstract:**

I will discuss some recent developments in canonical Ramsey theory in
the context of descriptive set theory. The talk
will be accessible to non-specialists.

Given a class **E** of Borel equivalence relations and a
sigma-ideal *I* on a Polish space *X*, we say that the
class **canonizes** to a finite set *{F _{1}, ... ,F_{n}}* of equivalence
relations if every Borel equivalence relation in
the class

This is joint work with Jindra Zapletal and Vladimir Kanovei.