Spring 2021 - Grigor Sargsyan
The Axiom of Determinacy (AD) says that all two player games of perfect information in which players play integers are determined. AD contradicts the Axiom of Choice but has many appealing consequence. Moreover, over the last 60 years it has become increasingly clear that determinacy of definable games is consistent with the usual axioms of set theory. The begining of such results was the original Gale-Steart theorem that all open games are determined, which was then extended by Martin to all Borel games. The Determinacy of more complicated games cannot be shown in ZFC alone. -- In this course, we will study the consequence of the Axiom of Determinacy. In a further course, we will study its connections with areas of mathematics.
basic graduate level mathematical maturity
Schedule of Sections:
- Fall 2019 Prof. Thomas
- Fall 2017 Prof. Thomas
Fall 2017 - Simon Thomas
Subtitle: Countable Borel Equivalence Relations
This course will be an introduction to countable Borel equivalence relations, a very active area of classical descriptive set theory which interacts nontrivially with such diverse areas of mathematics as model theory, computability theory, group theory and ergodic theory. The topics to be covered will include applications of superrigidity theory to countable Borel equivalence relations, as well as some recent applications of Borel determinacy. No prior knowledge of superrigidity or determinacy will be assumed.
Familiarity with the basic theory of complete separable metric spaces and their Borel subsets