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.

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.