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Kuratowski's lemma (Theorem)

Any chain in an ordered set is contained in a maximal chain.

This proposition is equivalent to the axiom of choice.



"Kuratowski's lemma" is owned by Koro.
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See Also: axiom of choice, Tukey's lemma, Zermelo's well-ordering theorem, Zorn's lemma, Zermelo's postulate, every vector space has a basis


Attachments:
equivalence of Kuratowski's lemma and Zorn's lemma (Proof) by CWoo
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Cross-references: axiom of choice, contained, chain
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This is version 3 of Kuratowski's lemma, born on 2002-12-09, modified 2004-01-31.
Object id is 3695, canonical name is KuratowskisLemma.
Accessed 3698 times total.

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