2012 seminar talk: Canonical Ramsey Theory on Polish Spaces
Talk held by Jindrich Zapletal (U of Florida, USA and Czech Academy of Sciences) at the KGRC seminar on 2012-05-24.
This is an update on the joint canonization program with Marcin Sabok and Vladimir Kanovei. For many classes of sigma-ideals I and many classes of analytic equivalence relations E there is a Borel I-positive set B such that E has a very simple form on B—such as B consists of pairwise inequivalent elements, or B consists of pairwise equivalent elements. In particular, this holds if I is a calibrated sigma-ideal generated by closed sets and E is an analytic equivalence relation.