# Tukey’s lemma

Each nonempty family of finite character has a maximal element.

Here, by a maximal element we a maximal element with respect to the inclusion ordering: $A\leq B$ iff $A\subseteq B$. This lemma is equivalent to the axiom of choice.

Title Tukey’s lemma TukeysLemma 2013-03-22 13:13:34 2013-03-22 13:13:34 Koro (127) Koro (127) 6 Koro (127) Theorem msc 03E25 AxiomOfChoice MaximalityPrinciple ZornsLemma ZermelosPostulate KuratowskisLemma