Grothendieck universe
transitive set closed under the operations of parameterized union, power set and unordered pairs
| rdfs:label |
"Grothendieck universe"@en
|
|
skos:alt |
"Universenaxiom"@de
|
| schema:description |
"transitive set closed under the operations of parameterized union, power set and unordered pairs"@en
|
|
schema:date |
"2026-09-08T10:49:11+00:00"^^xsd:dateTime |
| schema:version | 2542201282 |
| wikibase:identifiers | 4 |
| wikibase:sitelinks | 11 |
| wikibase:statements | 14 |
| p:P138 | wd:statement/Q1465090-f11de2b2-4549-27f2-248c-3df84c9861fa |
| p:P1889 | wd:statement/Q1465090-99df6a56-4bf8-649f-140c-0c7d8c10b260 |
| p:P2534 | wd:statement/Q1465090-EC5C433F-B227-4210-B2AA-E914DDC66360 |
| p:P2579 | wd:statement/Q1465090-4BD01F1B-1649-48D3-BDFA-586C8F15E7CA |
| p:P279 | wd:statement/Q1465090-3b56a5af-460d-9e38-952f-232324674ae5 |
| p:P31 | wd:statement/Q1465090-862440bc-4fa0-33f7-6b88-73c7c0e399bf |
| p:P4215 | wd:statement/Q1465090-6F329EB3-BEE0-4755-881F-961FCA53326E |
| p:P61 | wd:statement/Q1465090-c7ea3799-4822-3eee-c75e-67a411856435 |
| p:P6104 | wd:statement/Q1465090-00CD9A52-24FB-4ADA-8A70-257696DA2D55 |
| p:P6366 | wd:statement/Q1465090-A6627563-65AD-4F1B-8F0F-8414A29824DC |
| p:P646 | wd:statement/Q1465090-9FDED22B-1CF2-4134-9D3A-CE5C5AFE230C |
| p:P6781 | wd:statement/Q1465090-fc752bb0-44fe-dc4c-aa15-847e5fa2e142 |
| p:P7235 | wd:statement/Q1465090-d44b8950-401d-6b6e-eec0-155c1fe2dec6 |
| wd:statement/Q1465090-ed1d5c16-4e8f-5b24-24a4-45a88143f928 | |
|
p:direct- |
<https:/ |
| wdt:P138 | Alexander Grothendieck |
| wdt:P1889 | Universum |
| 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"><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>y</mi><mo stretchy="false">∈</mo><mi>U</mi><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi>x</mi><mo stretchy="false">∈</mo><mi>U</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mo fence="false" stretchy="false">{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo fence="false" stretchy="false">}</mo><mo stretchy="false">⊂</mo><mi>U</mi><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo fence="false" stretchy="false">{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo fence="false" stretchy="false">}</mo><mo stretchy="false">∈</mo><mi>U</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>U</mi><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒫</mi></mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">∈</mo><mi>U</mi><mo stretchy="false">∧</mo><mo fence="false" stretchy="false">{</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msub><mo fence="false" stretchy="false">}</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi></mrow></mrow></msub><mo stretchy="false">⊂</mo><mi>U</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><munder><mo stretchy="false">⋃</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi></mrow></mrow></munder><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">∈</mo><mi>U</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | category theory |
| wdt:P279 | transitive set |
| wdt:P31 | mathematical concept |
| wdt:P4215 | "Grothendieck universe" |
| wdt:P61 | Alexander Grothendieck |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2777712643" |
| wdt:P646 | "/m/043hbj" |
| wdt:P6781 | "Definition:Grothendieck_Universe" |
| 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"><mi>U</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"><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒫</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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