Math 6010 Fall 2024

(back to home)

Welcome to math 6010. This semester we will studying descriptive set theory with a focus on the theory of Borel equivalence relations, one of the active areas of modern logic. This area of mathematics is a somewhat recent development and incorporates methods from descriptive set theory, set theory, dynamics, and even geometric group theory and combinatorics.

We will begin the course with the basic descriptive set theory of Polish spaces. This will be a somewhat streamlined approach with the goal of introducing enough of the theory to move forward with the theory of Borel equivalence relations. We then introduce the main objects of study, Borel equivalence relations, and begin studying their properties.

For the first part of the course, where we give the background in descriptive set theory, the following set of notes may be useful: Polish spaces. A more extensive reference is Kechris' book Classical Descriptive Set Theory . I will be uploading additional content (various papers, etc.) as the course progresses.