MATH 468 - Introduction to Set Theory

Set-theoretical paradoxes and their modern resolution by Zermelo-Fraenkel set theory, ZF. The set-theoretic definitions of the natural numbers and the real numbers. Transfinite induction and recursion on well-founded sets. Higher infinities, ordinal and cardinal arithmetic, cofinality, the Axiom of Choice. An introductory exploration of questions of undecidability and relative consistency, including elements of the proof that the Axiom of Choice and the Continuum Hypothesis are consistent and thus cannot be disproven. Introductory discussion without proof of some more advanced modern results in set theory, including consistency of the negations of the Axiom of Choice and of the Continuum Hypothesis. Optional topics include large cardinals, infinitary combinatorics, and the Axiom of Determinacy.

Prerequisites: Grade of ‘C’ or better in MATH 357 - Linear Algebra.
Credit(s): 3
Course Attribute(s):

Honors Scholar Course.