## The Axiom of Choice, or: One Principle, Many Things

Leeds Pure Mathematics Postgraduate Seminar, 19th November 2015

Abstract:

I will discuss the infamous Axiom of Choice, the joker in the deck of the axioms of set theory. I will give examples of the following:

I will discuss the infamous Axiom of Choice, the joker in the deck of the axioms of set theory. I will give examples of the following:

- Some principles that are equivalent to it.
- Situations where you don't need it (but think you do).
- Situations where you do need it (but think you don't).
- Problematic and/or interesting consequences of it.
- Problematic and/or interesting consequences of its negation.
- Stuff in between (if I have time).