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# Tukey’s lemma

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.

Related:

AxiomOfChoice, MaximalityPrinciple, ZornsLemma, ZermelosPostulate, KuratowskisLemma

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

03E25*no label found*

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new question: Lorenz system by David Bankom

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new correction: examples and OEIS sequences by fizzie

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new correction: Closure properties on languages: DCFL not closed under reversal by babou

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new question: Latent variable by adam_reith

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith