A course on axiomatic set theory, emphasizing its dual role as a foundation upon which the rest of mathematics can be built, and as a rich subject in its own right, primarily concerned with the nature of the infinite. The axioms of Zermelo-Fraenkel Set Theory (ZFC); the interpretation of mathematical concepts, including the standard number systems, inside set theory; finite, countable, and uncountable sets; cardinal and ordinal numbers and their arithmetic; transfinite induction and recursion; the role of the Axiom of Choice; the cumulative hierarchy of sets. |