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 {F1, ... ,Fn} of equivalence
relations if every Borel equivalence relation in
the class E is equal to one of F1, ... ,Fn after a
restriction to a Borel set not in I. I will survey
recent canonization results for various classes of Borel equivalence
relations.
This is joint work with Jindra Zapletal and Vladimir Kanovei.