Basic Knowledge of Set Theory
Basic Descriptive Set Theory. We will cover topics in descriptive set theory that form foundations of modern classical descriptive set theory. Specific topics include determinacy, Silver's dichotomy theorem, HKL dichotomy, Kechris' proof the action of locally compact groups is classifiable by countable structures and etc.
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
Schedule of Sections:
For more information on instructors and sections for Fall 2017, please see our Fall 2017 Teaching Schedule Page
For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page