Continuous logic and Borel equivalence relations

Abstract: The theory of Borel reducibility of definable equivalence relations was initiated by Friedman and Stanley who were specifically interested in the equivalence relation of isomorphism of countable structures. Since then, the scope of the theory has considerably expanded but isomorphism of countable structures remains one of the situations where the most detailed results are available and where both methods of infinitary model theory and descriptive set theory can be applied. In this talk, I will explain how infinitary continuous logic can be used to extend parts of this theory to metric structures. Our main result is about isomorphism of locally compact metric structures and it is a common generalization of theorems of Hjorth (for locally compact metric spaces) and Hjorth and Kechris (for countable structures). This is joint work with Andreas Hallbäck and Maciej Malicki.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic