Place: Fields Institute (Room 210)
Date: March 23, 2018 (13:00-14:00)
Speaker: Slawomir Solecki
Title: Polishable equivalence relations
Abstract: We introduce the notion of Polishable equivalence relations. This class of equivalence relations contains all orbit equivalence relations induced by Polish group actions and is contained in the class of idealistic equivalence relations of Kechris and Louveau. We show that each orbit equivalence relation induced by a Polish group action admits a canonical transfinite sequence of Polishable equivalence relations approximating it. The proof involves establishing a lemma, which may be of independent interest, on stabilization of increasing ω1-sequences of completely metrizable topologies.