Syllabus
1. Historical background, axioms of ZFC.
2. Basic operations: inclusion, intersection, difference, pairs, cartesian product, relation, function.
3. Ordering, well-ordering, ordinal numbers, natural numbers, basics from ordinal arithmetic.
4. Countable and uncountable sets, cardinal numbers, Cantor-Bernstein theorem, cardinal arithmetics.
5. Classes and relations, transfinite induction and recursion.
6. Axiom of choice and its equivalents.
7. Elements of infinitary combinatorics: Konig's lemma, Compactness principle, Ramsey theorem. For details see https://iuuk.mff.cuni.cz/~samal/vyuka/1718/Sets/ In 2019/2020, there is an optional exercise for this course (Exercises from set theory - NAIL124).
Annotation
An introductory course to set theory.