# MATH 512 Advanced Topics in Logic: Descriptive Set Theory

## Fall 2012

Instructor: Dima Sinapova

Class Meets: MWF 11:00 - 11:50 in TH 320

Office: 421 SEO

Office Hours: MW 1-2

phone: (312)-996-2371

e-mail: sinapova@math.uic.edu

### Description

We will cover Polish spaces, definable subsets of Polish spaces: Borel, analytics, and projective sets, and definable equivalence relations.
We will go over dichotomy theorems and applications to classification problems in analysis and combinatorics.
Here is a tentative breakdown of topics:
- Polish spaces. Definitions, examples, basic properties, trees

- Regularity properties of Polish spaces. Infinite games and determinacy, the perfect set property, the Baire property, measurablity.

- Definable subsets of Polish spaces: Borel and analytic sets; the projective hierarchy

- Equivalence relations, dichotomy theorems, classification problems

### Text:

Descriptive set theory notes, by Anush Tserunyan PDF
### Homework and grading

There will be some homework assignments, which will be given in class or by email.