Classical set theory: Axioms of Zermelo-Fraenkel (ZF) set theory. Ordinal numbers, well-orderings and cardinal number theory in ZF. The Continuum Hypotheses. Independence results for ZF: permutation models and independence of the axiom of choice. Forcing and the independence of the Continuum. Boolean-valued models. Consequences of independence results for mathematics. A selection of the following subjects: Infinitary combinatorics, Gödel's constructible sets and the V=L axiom. Alternative axioms: Projective Determinacy and Martin's axiom. Large cardinals. Constructive set theory: CZF and IZF.
- Teacher: Erik Palmgren