Set Theory and Applications

(3 Credit Hours) · Undergraduate

This course is an introduction to set theory and its applications to other areas of mathematics. Textbook. A Course On Set Theory, by Ernest Schimmerling. Course Outline. (1) Brief introduction to mathematical logic. (2) Zermelo-Fraenkel Choice Axioms of mathematics. (3) Order. Well-orderings, ordinal numbers and ordinal arithmetic. (4) Cardinality. Cardinal numbers, cardinal arithmetic, and cofinality. (5) Trees. Topology fundamentals, the Baire space, ill-founded and well-founded trees, infinite games, Ramsey theory, and trees of uncountable height. (6) Dense linear orders. The rationals and the reals. (7) If time permits, we will cover additional topics.