Course Descriptions

16:640:566 - Axiomatic Set Theory

Simon Thomas

Course description:

In this course, we will study applications of Forcing Axioms to various classical problems in topology, algebra, cardinal arithmetic and the theory of uncountable trees. In particular, we will show that the Proper Forcing Axiom implies that \(2^{\aleph_{0}} = \aleph_{2}\).

Prereq:

Basic knowledge of ordinals and cardinals. A basic knowledge of set-theoretic forcing would also be helpful.

Text:

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