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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.

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Overview

Preliminaries

Statement

Consequences

Relationship to the incompleteness theorems

Relationship to the compactness theorem

Completeness in other logics

Proofs

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Gödel's completeness theorem

Nodes66
Edges65
Triples33
Avg. degree1.97
Density0.030303
Components1

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Gödel's completeness theorem

Top relations

related to Further reading · 27
Gödel's completeness theorem → Axiome, BF01696781, Chapter, Die Vollständigkeit, Doctoral, Funktionenkalküls, German, Gödel, Gödel's, Hans Hermes, Hochschultext, Introduction, ISBN, ISSN, JFM, Logikkalküls, London, Mathematical Logic, Mathematik, Monatshefte
related to Proofs · 3
Gödel's completeness theorem → Gödel's, Henkin's, In
see also · 2
Gödel's completeness theorem → Gödel's, Original
is a · 1
Gödel's completeness theorem → fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.The completeness theorem applie…

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Important terminology

theorem completeness model proof theory deductive system displaystyle first-order logic provable gödel's formula compactness consequence also existence logically valid sentence

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Gödel's completeness theoremis afundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.The completeness theorem applie…0.90text
Gödel's completeness theoremrelated to Further readingGödel0.60section
Gödel's completeness theoremrelated to Further readingVollständigkeit0.60section
Gödel's completeness theoremrelated to Further readingLogikkalküls0.60section
Gödel's completeness theoremrelated to Further readingThesis0.60section
Gödel's completeness theoremrelated to Further readingDoctoral0.60section
Gödel's completeness theoremrelated to Further readingUniversity Of Vienna0.60section
Gödel's completeness theoremrelated to Further readingThe0.60section
Gödel's completeness theoremrelated to Further readingDie Vollständigkeit0.60section
Gödel's completeness theoremrelated to Further readingAxiome0.60section
Gödel's completeness theoremrelated to Further readingFunktionenkalküls0.60section
Gödel's completeness theoremrelated to Further readingMonatshefte0.60section

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