MATH 511 Advanced Topics in Logic: Descriptive Set Theory

Spring 2018

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.