Department of

# Mathematics

Seminar Calendar
for Model Theory and Descriptive Set Theory Seminar events the next 2 months of Saturday, March 24, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2018            March 2018             April 2018
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1  2  3                1  2  3    1  2  3  4  5  6  7
4  5  6  7  8  9 10    4  5  6  7  8  9 10    8  9 10 11 12 13 14
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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.

Friday, May 4, 2018

4:00 pm in 345 Altgeld Hall,Friday, May 4, 2018

#### Analytic hypergraphs and proper forcing

###### Jindrich Zapletal (University of Florida Math)

Abstract: Given a countable family $G$ of analytic hypergraphs on a Polish space $X$, one can consider the quotient poset $P(G)$ of Borel sets modulo the ideal generated by Borel sets which are anticliques in at least one hypergraph in $G$. This is a broad family of forcings, many of them proper. The family is closed under such operations as countable support iteration of (in some cases) product. Most traditional fusion arguments disappear in this class of forcing. They are replaced by simple combinatorial considerations about the edges of the generating hypergraphs.