Basic operations between sets. Equinumerosity. Russel's paradox and the ZFC axiomatic system. Ordered pairs, relations and functions. Natural numbers: existence, uniqueness, fundamental properties, induction and recursion. Partially ordered spaces and Fixed Point theorems. Well-ordered spaces: fundamental properties, transfinite induction and recursion. Axiom of Choice and equivalent statements. Basic cardinal arithmetic. Replacement Axiom. Ordinal numbers and basic results.
- Teacher: Βασίλειος Γρηγοριάδης
ECTS : 5
Language : el