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
| rdfs:label |
"Zorn's lemma"@en
|
|
skos:alt |
"Kuratowski–Zorn lemma"@en
|
| schema:description |
"statement equivalent to the axiom of choice, about the existence of a maximal element in a poset with a maximal chain condition"@en
|
|
schema:date |
"2025-12-06T10:39:31+00:00"^^xsd:dateTime |
| schema:version | 2438726649 |
| wikibase:identifiers | 13 |
| wikibase:sitelinks | 35 |
| wikibase:statements | 27 |
| p:P10376 | wd:statement/Q290810-E8384FEE-C1C7-4027-A559-F6E5BA678618 |
| p:P1051 | wd:statement/Q290810-19043220-50A9-4C78-B744-808945B5291A |
| p:P11514 | wd:statement/Q290810-648616B4-00FD-473B-8C5C-98752F673D19 |
| p:P12385 | wd:statement/Q290810-28b618df-f0c7-4a78-9f7d-168700b1483b |
| p:P1296 | wd:statement/Q290810-853673F8-DD1A-434C-8DE6-9AAAD434C0DD |
| p:P138 | wd:statement/Q290810-d57d7bed-424f-301c-f3ea-4bf8228f86af |
| wd:statement/q290810-edfedca6-4e76-4e7b-5a48-e67fd1c80076 | |
| p:P1417 | wd:statement/Q290810-4efc34d3-4192-37ce-cdb5-80222ed8ea5c |
| p:P2534 | wd:statement/Q290810-04ef08ec-4f3e-ec17-a544-618f7284543e |
| p:P2579 | wd:statement/Q290810-ccdbabf1-40b3-bd5e-cf92-7307f9987c79 |
| p:P2812 | wd:statement/Q290810-76198ce3-4ea6-0eba-8443-4b42789b4b10 |
| p:P31 | wd:statement/Q290810-138df82f-4802-bb3e-be32-bc884fe5e247 |
| wd:statement/Q290810-87ed97d8-4859-1ad9-94a9-e09db96ef6a2 | |
| p:P361 | wd:statement/Q290810-BEBCA8CC-36B8-4159-B3AC-411CF5105CB5 |
| p:P4215 | wd:statement/Q290810-CBC3AC51-A591-4E4D-807F-8E70C856261A |
| p:P460 | wd:statement/Q290810-86348276-4690-b31b-238d-eab5709befcb |
| p:P6104 | wd:statement/Q290810-956E2B82-10EA-4A80-A8EF-FE1A8F0670A1 |
| p:P6366 | wd:statement/Q290810-D03F245C-3BA4-4186-8F17-278ED37975A7 |
| p:P646 | wd:statement/Q290810-22E350DF-D839-4297-8F7E-E7D6563F5737 |
| p:P6781 | wd:statement/Q290810-d77800dc-4c98-5111-4de1-eccee44fe6f4 |
| p:P7235 | wd:statement/Q290810-7d987aa1-4bea-d681-5c42-5a7adfc3d488 |
| wd:statement/Q290810-9bf4039a-46b3-8884-0b6f-bbd66050b693 | |
| wd:statement/Q290810-d38ee87d-4dfd-02bf-1759-2cf586ca791b | |
| wd:statement/Q290810-e7467f33-44eb-837e-02df-ab2467b06e65 | |
| p:P7719 | wd:statement/Q290810-a1306e72-4257-3d50-2f59-64585a98507b |
| p:P8313 | wd:statement/Q290810-F0B716B4-099A-4EB8-969C-9A2F55BCE3BD |
| p:P9621 | wd:statement/Q290810-7C5DBA6D-D8D5-4D00-999A-361D1187E60D |
|
p:direct- |
<https:/ |
| wdt:P10376 | "mathematics/zorn-lemma" |
| wdt:P1051 | "7138" |
| wdt:P11514 | "lemma-tsorna-1107e6" |
| wdt:P12385 | "lema-de-zorn" |
| wdt:P1296 | "0073388" |
| wdt:P138 | wd:Q161846 |
| wd:Q58676 | |
| wdt:P1417 | "topic/Zorns-lemma" |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">∀</mi><mi>C</mi><mo stretchy="false">⊂</mo><mi>P</mi><mo stretchy="false">:</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>c</mi><mo>,</mo><msup><mi>c</mi><mo>′</mo></msup><mo stretchy="false">∈</mo><mi>C</mi><mo stretchy="false">:</mo><mi>c</mi><mo stretchy="false">≤</mo><msup><mi>c</mi><mo>′</mo></msup><mo stretchy="false">∨</mo><mi>c</mi><mo stretchy="false">≥</mo><msup><mi>c</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∃</mi><mi>u</mi><mo stretchy="false">∈</mo><mi>P</mi><mo stretchy="false">:</mo><mi>C</mi><mo stretchy="false">≤</mo><mi>u</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∃</mi><mi>m</mi><mo stretchy="false">∈</mo><mi>P</mi><mi mathvariant="normal">∀</mi><mi>p</mi><mo stretchy="false">∈</mo><mi>P</mi><mo stretchy="false">:</mo><mi>m</mi><mo stretchy="false">≰</mo><mi>p</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | wd:Q12482 |
| wdt:P2812 | "ZornsLemma" |
| wdt:P31 | wd:Q207505 |
| wd:Q4478785 | |
| wdt:P361 | wd:Q3632199 |
| wdt:P4215 | "Zorn's lemma" |
| wdt:P460 | wd:Q179692 |
| wdt:P6104 | wd:Q8487137 |
| wdt:P6366 | "78538056" |
| wdt:P646 | "/m/0dkrp" |
| wdt:P6781 | "Zorn's_Lemma" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">≤</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>C</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>m</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>P</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P7719 | wd:Q179692 |
| wdt:P8313 | "Zorns_lemma" |
| wdt:P9621 | "lemma-di-zorn" |
Inverse relations
[ .. ] → p:statement/P7719 → Zorn's lemma
[ .. ] → schema:about → Zorn's lemma
Beweisarchiv: Mengenlehre: Lemma von Zornschema:Article
Bổ đề Zornschema:Article
Kuratowski-Zornova lemaschema:Article
Lema da Zornschema:Article
Lema de Zornschema:Article
Lema de Zornschema:Article
Lema de Zornschema:Article
Lema de Zornschema:Article
Lema lui Zornschema:Article
Lema Zornschema:Article
Lemat Kuratowskiego-Zornaschema:Article
Lemma di Zornschema:Article
Lemma van Zornschema:Article
Lemma von Zornschema:Article
Lemme de Zornschema:Article
Princip maximalityschema:Article
Set Theory/Zorn's Lemma and the Axiom of Choiceschema:Article
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Zorn's lemmaschema:Article
Zorn-lemmaschema:Article
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