Gödel's completeness theorem
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first order theory: If T is such a theory, and φ is a sentence (in the same language) and any model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything true is provable."
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1929 in scienceAutomated theorem provingAxiomAxiom of choiceCipher Department of the High Command of the WehrmachtCompactness theoremComplete theoryCompleteness (logic)Completeness theoremComputability theoryDecidability (logic)Elementary classElementary definitionEntscheidungsproblemFinite model theoryFirst-order logicFoundations of mathematicsGentzen's consistency proofGisbert HasenjaegerGlossary of set theoryGodel's completeness theoremGodel completeness theoremGoedel's completeness theoremGoedel completeness theoremGoedels completeness theoremGödel's incompleteness theoremsGödel's theoremGödel completeness theoremHigher-order logicHistory of logicIndex of philosophy articles (A–C)Inner modelInstitutional model theoryIsabelle (proof assistant)Kurt GödelLeon HenkinLindenbaum's lemmaList of cryptographersList of first-order theoriesList of mathematical logic topics
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Gödel's completeness theorem
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first order theory: If T is such a theory, and φ is a sentence (in the same language) and any model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything true is provable."
has abstract
De volledigheidsstelling van G ...... n volledigheid verwezen wordt.
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Der Gödelsche Vollständigkeits ...... che Folgerung gleichbedeutend.
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El teorema de completitud de G ...... fue simplificada por en 1953.
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En logique mathématique, le th ...... t conséquence syntaxique de T.
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Gödel's completeness theorem i ...... y Gisbert Hasenjaeger in 1953.
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Gödelova věta o úplnosti predi ...... ký pojem pravdivosti v modelu.
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Il Teorema di completezza di G ...... la verità della sua negazione.
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O Teorema da completude de Göd ...... tido pelo Teorema da correção.
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Теоре́ма Гёделя о полноте́ исч ...... зуема в исчислении предикатов.
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Теорема Геделя про повноту — т ...... засад побудови теорії моделей.
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comment
De volledigheidsstelling van G ...... n volledigheid verwezen wordt.
@nl
Der Gödelsche Vollständigkeits ...... che Folgerung gleichbedeutend.
@de
El teorema de completitud de G ...... te una computadora, o a mano).
@es
En logique mathématique, le th ...... t conséquence syntaxique de T.
@fr
Gödel's completeness theorem i ...... s "anything true is provable."
@en
Gödelova věta o úplnosti predi ...... ký pojem pravdivosti v modelu.
@cs
Il Teorema di completezza di G ...... ando gli assiomi della teoria.
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O Teorema da completude de Göd ...... aplicadas a passos anteriores.
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Теоре́ма Гёделя о полноте́ исч ...... зуема в исчислении предикатов.
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Теорема Геделя про повноту — т ...... ні через предикативні формули.
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Gödel's completeness theorem
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Gödelova věta o úplnosti predikátové logiky
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Gödelscher Vollständigkeitssatz
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Teorema da completude de Gödel
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Teorema de completitud de Gödel
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Teorema di completezza di Gödel
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Théorème de complétude de Gödel
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Volledigheidsstelling van Gödel
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Теорема Геделя про повноту
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Теорема Гёделя о полноте
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