# Math Department Seminar - Kechris

Seminar of the Department of Mathematics

Speaker: **Alekos Kechris**, **Caltech**

**Friday, June 30, 2017, 14:30, Room Γ32**

**«** Borel equivalence relations, cardinal algebras and structurability»

**Abstract: **The theory of Borel equivalence relations has been a very active area of research in descriptive set theory during the last 25 years. In this talk, I will discuss how Tarski’s concept of cardinal algebras, going back to the 1940’s, appears naturally in this theory and show how Tarski’s theory can be used to discover new laws concerning the structure of Borel equivalence relations, which, rather surprisingly, have not been realized before. In addition, I will discuss the concept of structurability for equivalence relations and explain some of its implications concerning the algebraic structure of the reducibility order among such equivalence relations. (This is joint work with H. Macdonald and R. Chen.)