Julian Mauersberger: The Axiom of Choice

In the history of Mathematics, the Axiom of Choice (AC) has been one of the most controversial axioms. Nevertheless, over the years the proponents seem to have won the debate and nowadays most mathematical work is based on Zermelo-Fraenkel (ZF) set theory with AC. In my talk I will recall AC, equivalents, and the foundations of set theory on a basic level in order to explore the both fabulous and frightening world of ZF without AC.