Course Descriptions

16:640:566 - Axiomatic Set Theory

Grigor Sargsyan

Subtitle:

Proofs of determinacy

Course description:

Thinking of reals as point in the Baire space N^N, consider the two player game with payoff set A subset N^N in which players collaborate to produce a real x and player I wins it x is in A.

Axiom of Determinacy is the statement that all games as above are determined, i.e., one of the players has a winning strategy.

AC implies that AD is false, but definable versions of AD are true. For example a classic theorem of Martin says that all Borel games are determined.

In this course we will develop techniques for proving the determinacy of definable games. Along the way we will develop many tools needed for doing research in set theory.

Prereq:

graduate level mathematical maturity and some set theory

Text:

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