Descriptive Set Theory

Course content

Topological preliminaries. Polish spaces, compact metric spaces, zero-dimensional spaces and Baire category methods. Measurable spaces and standard Borel spaces. Borel hierarchy, Borel sets and their regularity properties, and the Borel isomorphism theorem. Projective sets, analytic and coanalytic sets, and their regularity properties. Separation theorems. Polish groups. Selected topics: Borel determinacy, various uniformization theorems, theory of Borel equivalence relations etc.