Abstract:
This will be the first of a series of talks investigating the Axiom of
Choice for Finite Sets [KC] in the context of topos theory.
Classically, KC follows from the Linear Ordering Principle, which is a
consequence of the Prime Ideal Theorem, which is usually proven using
Zorn's Lemma. So it seems appropriate to begin with a reminder of
what is known about Zorn's Lemma in toposes, and in particular, how it
differs from the Axiom of Choice.