PlanetMath: Tukey's lemma

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Tukey's lemma

(Theorem)

Each nonempty family of finite character has a maximal element.

Here, by a maximal element we mean 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.

"Tukey's lemma" is owned by Koro.

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Cross-references: axiom of choice, equivalent, iff, ordering, inclusion, maximal element, finite character
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This is version 3 of Tukey's lemma, born on 2002-12-09, modified 2002-12-09.
Object id is 3693, canonical name is TukeysLemma.
Accessed 3229 times total.

Classification:

03E25 (Mathematical logic and foundations :: Set theory :: Axiom of choice and related propositions)

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