MATH 354 Set Theory and Foundations of Mathematics

Cantor's naïve theory of sets and equinumerosity. Paradoxes and axiomatic set theory. Finite and infinite cardinal numbers, fixed point theory, applications to computer science. Well orderings, transfinite induction and recursion, the Axiom of Choice and its consequences, ordinal numbers, and the cumulative hierarchy of sets. Discussion of the Continuum Hypothesis and its relation to models of set theory.