Cornell Math - MATH 787, Spring 2005

MATH 787: Set Theory (Spring 2005)

Instructor: Richard Shore

Meeting Time & Room

This course will be a basic introduction to axiomatic set theory beginning with the axioms for Zermelo-Fraenkel Set theory and the elementary theory of ordinal and cardinal numbers. We will develop enough of the structure of Goedel's constructible universe L to prove the consistency of the general continuum hypothesis, the axiom of choice and various combinatorial principles useful for establishing consistency results in topology and algebra (e. g. the Souslin and Whitehead problems). We will also investigate some of the forcing constructions of Cohen, Martin, Solovay and others to construct models of set theory in which the continuum hypothesis fails and various problems of combinatorics, topology and algebra have different solutions than they do in Goedel's universe. There may also be some discussion of combinatorial properties of some of what are now considered to be the smaller of the large cardinals.

Prerequisites: A familiarity with predicate logic and naive set theory.

Text:Set Theory, An Introduction to Independence Proofs, K. Kunen