Set Theory - SET

Instructor: Dr. Lajos SOUKUP

Text: The course is based on printed handouts distributed in class.

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

Course description:
This course is designed as an introduction to basic set theoretic notions and methods.

Course outline
Introduction. Elementary Set Theory
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.
Applications in algebra, analysis, combinatorics and geometry
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:

Homepage of the course: