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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 collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia