Set Theory — SET

Instructor: Dr. Lajos SOUKUP

Text: The course is based on printed handouts

Prerequisite: Some familiarity with "higher" mathematics. No specific knowledge is expected.

Course description:
This course is designed as an introduction to basic concepts of Set Theory. We learn how to use set theory as a powerful tool in algebra, analysis, combinatorics, and even in geometry.

Course outline
Introduction. Set theory as the study of infinity.
Countable sets and their combinatorics.
Cardinalities. Cardinal arithmetic.
Axiom of Choice. Ordered and well-ordered sets. Zorn lemma and its applications.
Well-ordering Theorem. Transfinite induction and recursion.
Ordinals, ordinals arithmetic and its applications.
Cardinalities revisited. Cofinalities.
Infinite combinatorics. Continuum hypothesis.
Axiomatic set theory.

Learning Outcomes
After successfully completing the course, the student should be able to:

A. Shen, and N. K. Vereshchagin, Basic Set Theory, AMS Student Mathematical Library 17,
P. Halmos: Naive Set Theory
P. Hamburger, A. Hajnal: Set Theory
K. Ciesielski: Set Theory for the Working Mathematician