Course Descriptions

16:640:566 - Axiomatic Set Theory

Spring 2020 - 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.

Text:

None

Prerequisites:

graduate level mathematical maturity and some set theory

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Spring 2019 Simon Thomas

Subtitle:

Set-theoretic forcing: an introduction to independence proofs

Course description:

This is an introductory course on proving independence results in set theory. Here a statement S is said to be independent of set theory if S can neither be proved nor disproved from the classical ZFC axioms of set theory. For example, we will show that the Continuum Hypothesis CH is independent of set theory.

Text:

Kenneth Kunen, Set Theory: An Introduction to Independence Proofs, North Holland, Amsterdam

Prerequisites:

A knowledge of basic set theory, including cardinals, ordinals and the axiom of choice.

Schedule of Sections

Previous Semesters: