Zorn's lemma
statement equivalent to the axiom of choice, about the existence of a maximal element in a poset with a maximal chain condition
Facts
9 properties- Instance of
- lemma, equivalent of the axiom of choice[2]
- Part of
- list of axioms[5]
- Defining formula
- \left(\forall C\subset P\colon(\forall c,c'\in C\colon c\le c'\lor c\ge c')\implies\exists u\in P\colon C\le u\right)\implies\exists m\in P\forall p\in P\colon m\not\le p[7]
- Generalization of
- axiom of choice[14]
- Maintained by WikiProject
- WikiProject Mathematics[9]
- Named after
- Max August Zorn, Kazimierz Kuratowski[3][4]
- Said to be the same as
- axiom of choice[6]
- Studied by
- set theory[8]
🏷️ Also known as
en Kuratowski–Zorn lemma
en Zorn's lemma
cs princip maximality
da Zorns lemma
de Lemma von Zorn
de Zornsches Lemma
de Lemma von Kuratowski–Zorn
el Λήμμα του Zorn
es lema de Zorn
fa لم زرن
fi Kuratowskin-Zornin lemma
fi Zornin lemma
fr lemme de Kuratowski–Zorn
fr lemme de Zorn
fr théorème de Zorn
he הלמה של צורן
hu Zorn-lemma
id lemma (matematika)
id lemma Zorn
it lemma di Zorn
🔖 Identifiers · 13
- Encyclopædia Britannica Online ID
- topic/Zorns-lemma
- Freebase ID
- /m/0dkrp
- Gran Enciclopèdia Catalana ID
- lema-de-zorn
- Gran Enciclopèdia Catalana ID (former scheme)
- 0073388
- Great Russian Encyclopedia portal ID
- lemma-tsorna-1107e6
- Lex ID
- Zorns_lemma
- MathWorld ID
- ZornsLemma
- Microsoft Academic ID (discontinued)
- 78538056
- NLab ID
- Zorn's lemma
- PSH ID
- 7138
- ProofWiki ID
- Zorn's_Lemma
- ScienceDirect topic ID
- mathematics/zorn-lemma
Show all 13 identifiers +1
- Treccani's Enciclopedia della Matematica ID
- lemma-di-zorn
🔗 Connections
Named after 2
Created notable works 1
Generalization of 1
Instance of 1
Maintained by WikiProject 1
Said to be the same as 1
Studied by 1
← Generalization of 1
← Said to be the same as 1
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Summary
Zorn's lemma is a lemma[1].