Tukey’s lemma

Each nonempty family of finite character has a maximal elementMathworldPlanetmath.

Here, by a maximal element we a maximal element with respect to the inclusion orderingMathworldPlanetmath: AB iff AB. This lemma is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to the axiom of choiceMathworldPlanetmath.

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