Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 20, 2018.

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Friday, April 20, 2018

4:00 pm in 345 Altgeld Hall,Friday, April 20, 2018

#### Polishable Borel equivalence relations

###### Sławomir Solecki (Cornell)

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 $\omega_1$-sequences of completely metrizable topologies.