The topic for this course is descriptive set theory. The course will concentrate on applications of determinacy, that is the assertion that in all infinite, perfect information two player games of a given complexity, one of the players has a wining strategy.
Time: Thursdays 3pm to 4:50pm.
Place: MS 6118.
Contact: Itay Neeman.
Office: MS 6334.
Office hours: Monday and Wednesdays, 1pm to 2pm.
Topics and speakers: (List updated as the term progresses.)
Under the full axiom of determinacy, all sets of reals are Lebesgue measurable. Proof from the paper A simple proof that determinancy implies Lebesgue measurability by D.A. Martin, presented by Justin Palumbo.
Uniformization property for pointclasses, and propagation of the scale property. From the book Descriptive Set Theory by Yiannis Moschovakis, presented by Yoann Dabrowski.
Guest lecture. Dilip Raghavan, on cardinal invariants of the continuum and the existence of a van Douwen family.
Wellfoundedness of the Wadge hierarchy, from the book Descriptive Set Theory by Yiannis Moschovakis, and separation properties under the axiom of determinacy, from the papers Determinateness and the separation property by Steel, and Separation principles and the axiom of determinateness by Van Wesep, presented by Konstantinos Palamourdas.
Pure strategy determinacy for perfect information games implies mixed strategy determinacy for imperfect information games, from the paper The determinacy of Blackwell games by D.A. Martin, presented by Darren Cruetz.
Mixed strategy determinacy implies pure strategy determinacy in L(R), from the paper The strength of Blackwell determinacy by Martin, Neeman, and Vervoort, presented by Anush Tserunyan.