UWEC CERCA 2025

Zorn's Lemma was proven under the assumption of the Axiom of Choice in 1922 by Kazimierz Kuratowksi, but was proven without well-ordering in 1935 by Max August Zorn. The Axiom of Choice states that for any collection of sets, a choice function exists. Zorn's Lemma states that in every nonempty partially ordered set with upper bounds for each chain, there exists a maximal element. These claims are in fact equivalent. In this presentation, we will introduce basic set theory notions, prove the equivalence of the Axiom of Choice and Zorn's Lemma, and show its applications in other disciplines of mathematics.