MATH 512 Advanced Topics in Logic: Descriptive Set Theory
Instructor: Dima Sinapova
Class Meets: MWF 11:00 - 11:50 in TH 320
Office: 421 SEO
Office Hours: MW 1-2
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.