Suslin's problem
the proposition, independent of ZFC, that a nonempty unbounded complete dense total order satisfying the countable chain condition is isomorphic to the reals
| rdfs:label |
"Suslin's problem"@en
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skos:alt |
"problemo de Suslin"@eo
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| schema:description |
"the proposition, independent of ZFC, that a nonempty unbounded complete dense total order satisfying the countable chain condition is isomorphic to the reals"@en
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schema:date |
"2026-08-05T22:16:46+00:00"^^xsd:dateTime |
| schema:version | 2527835690 |
| wikibase:identifiers | 2 |
| wikibase:sitelinks | 12 |
| wikibase:statements | 14 |
| p:P138 | wd:statement/q2296408-3d482f36-4862-4285-3e35-fd69ee3f3d4d |
| p:P14434 | wd:statement/Q2296408-969df58d-2297-4b5b-95dd-e206aaf06950 |
| p:P2534 | wd:statement/Q2296408-96a2bfb6-4364-7d95-5a97-8b8eecff611f |
| p:P31 | wd:statement/Q2296408-6a001df8-4e79-4ba3-10c3-8d4211760159 |
| p:P361 | wd:statement/Q2296408-A24D7EA4-632A-46AC-B3B2-46A7ADED09E6 |
| p:P577 | wd:statement/Q2296408-53f5fd7b-42de-c67a-6b2a-503a22a9c53e |
| p:P61 | wd:statement/Q2296408-E207059F-4E45-49C5-9C86-85AAC575893E |
| p:P6104 | wd:statement/Q2296408-786DBEB1-A069-4BB5-8491-3F3B5E861609 |
| p:P6366 | wd:statement/Q2296408-7603E933-D7E7-48D4-97A9-E59B40A0D955 |
| p:P646 | wd:statement/Q2296408-7745CE59-B0DD-4DEC-82AB-14834F028D18 |
| p:P7235 | wd:statement/Q2296408-6c7eb877-46ac-483b-63a3-8a02e84a12c7 |
| wd:statement/Q2296408-7d1ece0b-49d4-e030-1be6-6b2720a8c9d4 | |
| wd:statement/Q2296408-a3439df8-4405-333b-d403-188bf87df0f5 | |
| wd:statement/Q2296408-ee55b93d-4917-7eff-6d8c-3620cc615e91 | |
|
p:direct- |
<https:/ |
| wdt:P138 | Mikhail Suslin |
| wdt:P14434 | list of values as qualifiers |
| 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"><mi>X</mi><mo stretchy="false">≅</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow><mo>,</mo><mo stretchy="false">≤</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo stretchy="false">|</mo><mi>X</mi><mo stretchy="false">|</mo><mo>></mo><mn>0</mn><mo stretchy="false">∧</mo><mi mathvariant="normal">∃</mi><mi>max</mi><mo>⁡</mo><mi>X</mi><mo stretchy="false">∧</mo><mi mathvariant="normal">∃</mi><mi>min</mi><mo>⁡</mo><mi>X</mi><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">∈</mo><mi>X</mi><mo stretchy="false">:</mo><mi>x</mi><mo><</mo><mi>y</mi><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">≠</mo><mi variantform="True">∅</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>S</mi><mo stretchy="false">⊂</mo><mi>X</mi><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi><mo stretchy="false">:</mo><mo stretchy="false">(</mo><mi>S</mi><mo><</mo><mi>x</mi><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>sup</mi><mo>⁡</mo><mi>S</mi><mo stretchy="false">∧</mo><mi>x</mi><mo><</mo><mi>S</mi><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>inf</mi><mo>⁡</mo><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>I</mi><mi mathvariant="normal">∀</mi><mi>a</mi><mo>,</mo><mi>b</mi><mo stretchy="false">:</mo><mi>I</mi><mo stretchy="false" accent="false">→</mo><mi>X</mi><mo stretchy="false">:</mo><mo stretchy="false">(</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">:</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo><</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi mathvariant="normal">∀</mi><mi>i</mi><mo stretchy="false">≠</mo><mi>j</mi><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">:</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi variantform="True">∅</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><mo stretchy="false">|</mo><mi>I</mi><mo stretchy="false">|</mo><mo><</mo><msub><mi mathvariant="normal">ℵ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P31 | conjecture |
| wdt:P361 | descriptive set theory |
| wdt:P577 | "1920-01-01T00:00:00+00:00"^^xsd:dateTime |
| wdt:P61 | Mikhail Suslin |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2775894269" |
| wdt:P646 | "/m/01h959" |
| 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>X</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"><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"><mo stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>b</mi><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"><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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