Definition
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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set theoryContinuum hypothesisCountableCountable setDavid HilbertDecidability (logic)Decision problemDeductive systemDiagram (mathematical logic)Domain of a functionEffective methodEffectively computableElement (mathematics)Elementary diagramElementary equivalenceElementary function arithmeticEmpty setEntscheidungsproblemEnumerationEquiconsistencyEquivalence relationEuclid's ElementsEuclidean geometryExistential quantificationExpression (mathematics)Extension by definitionsExtension by new constant and function namesExtensionalityFinitary relationFinite-valued logicFinite model theoryFinite setFirst-order logicFixed-point logicForcing (mathematics)Formal grammarFormal languageFormal proofFormal semantics (logic)Formal systemFormation ruleFoundations of geometryFoundations of mathematicsFree logicFree variables and bound variablesFunction (mathematics)Functional predicateFuzzy setGeneral set theoryGisbert HasenjaegerGrothendieck universeGround expressionGround formulaGroup theoryGödel's incompleteness theoremGödel's incompleteness theoremsGödel numberingHalting problemHans HermesHenkin semanticsHereditary setHigher-order logicHilbert's axiomsHilbert-style deduction systemHilbert systemHistory of logicHistory of mathematical logicIf and only ifImage (mathematics)Inaccessible cardinalIndependence (mathematical logic)InferenceInfinite-valued logicInfinite setInformation theoryInhabited setInjective functionInterpretation (logic)Interpretation (model theory)Interpretation functionIntersection (set theory)Intuitionistic logicIsabelle (theorem prover)IsomorphismJuliette KennedyKolmogorov complexityKripke's theory of truthKripke semanticsKripke–Platek set theoryKurt GödelLambda calculusLarge cardinalLemma (mathematics)Leon HenkinLindenbaum's lemmaLindström's theoremList of Hilbert systemsList of axiomsList of first-order theoriesList of formal systemsList of mathematical theoriesList of set identities and relationsList of statements independent of ZFCLogicLogical 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(logic)T-schemaTarski's axiomatization of the realsTarski's axiomsTarski's theory of truthTarski's undefinability theoremTarski–Grothendieck set theoryTautology (logic)Tennenbaum's theoremTerm (logic)Term logicThe Journal of Symbolic LogicTheoremTheories of truthTheory (mathematical logic)Three-valued logicTimeline of mathematical logicTrakhtenbrot's theoremTransfer principleTransitive setTree structureTrue arithmeticTruth predicateTruth tableTruth valueTuring machineType (model theory)Type theoryType–token distinctionUltrafilter (set theory)UltraproductUncountable setUndecidable problemUninterpreted functionUnion (set theory)Uniqueness quantificationUniversal quantificationUniversal setUniverse (mathematics)UrelementUse–mention distinctionValidity (logic)Variable (mathematics)Venn diagramVon Neumann universeVon Neumann–Bernays–Gödel set theoryWeak Kőnig's lemmaWell-formed formulaWell-orderWilhelm AckermannZermelo–Fraenkel set theory
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