Itay Kaplan: The Borel Cardinality of model theoretic equivalence relations

Logic Seminar (HUJI)

The speaker on December 18 is Itay Kaplan.
Title: The Borel Cardinality of model theoretic equivalence relations
Abstract: Invariant equivalence relations are very important in model theory, especially when they are bounded, i.e., when the number of classes is small. The canonical such relations are the Shelah, Kim-Pillay and the Lascar strong types equivalence relations. While the first two give rise to a compact Hausdorff topological space, the third one generally does not.
It turns out that one can look at equality of Lascar strong types through descriptive set theory, where it is a K_sigma equivalence relation on a Polish space, and it can be given a precise “Borel cardinality”, i.e., it’s place in the quasi order of Borel reducibility.
In the talk I will define all of these notions and will present some results, the main one being that the Lascar equivalence relation is either closed or non-smooth.
I will also discuss other equivalence relations, such as those coming from group actions.

The logic seminar  takes place on Wednesdays at 16:00, in room 209.

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