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: $A\le B$ iff $A\subseteq B$. This lemma is equivalent to the axiom of choice.

Title	Tukey’s lemma
Canonical name	TukeysLemma
Date of creation	2013-03-22 13:13:34
Last modified on	2013-03-22 13:13:34
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Theorem
Classification	msc 03E25
Related topic	AxiomOfChoice
Related topic	MaximalityPrinciple
Related topic	ZornsLemma
Related topic	ZermelosPostulate
Related topic	KuratowskisLemma