blanketglossary

Löwenheim–Skolem theorem

Definition

In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem.

Related concepts

Absoluteness (mathematical logic)Abstract logicAckermann set theoryAleph numberAlfred TarskiAlgebraic logicAlonzo ChurchAlphabet (formal languages)Anatoly MaltsevArgumentArityAssociation for Symbolic LogicAtomic formulaAtomic model (mathematical logic)Atomic sentenceAutomata theoryAutomated theorem provingAxiomAxiom of choiceAxiom schemaAxiomatic systemAxiomatization of Boolean algebrasBanach–Tarski paradoxBerlinBijectionBinary operationBoca Raton, FloridaBoolean algebraBoolean algebras canonically definedBoolean functionCRC PressCalculus of relativesCambridgeCambridge University PressCantor's diagonal argumentCantor's paradoxCantor's theoremCardinal numberCardinalityCartesian productCategorical theoryCategory (mathematics)Category of setsCategory theoryCharles Sanders PeirceChen Chung ChangChurch encodingChurch–Turing thesisClass (set theory)Classical logicClosure operatorCodomainCompactness theoremComplement (set theory)Complete theoryCompleteness (logic)Computability theoryComputable functionComputable setComputably enumerable setConcrete categoryConservative extensionConsistencyConstructible universeConstruction of the real numbersConstructive set theoryContinuum hypothesisCooper Harold LangfordCountableCountable setDecidability (logic)Decision problemDeductive systemDiagram (mathematical logic)Domain of a functionDover PublicationsEffective methodElement (mathematics)Elementary diagramElementary equivalenceElementary function arithmeticElementary substructureEmpty setEntscheidungsproblemEnumerationEquiconsistencyEquivalence relationEric W. WeissteinErnst Schröder (mathematician)Euclid'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 theoryGeneseo, New YorkGoogle BooksGrothendieck universeGround expressionGround formulaGödel's completeness theoremGödel's incompleteness theoremGödel's incompleteness theoremsGödel numberingHalting problemHeidelbergHereditary setHigher-order logicHilbert's axiomsHilbert systemHistorical revisionismHistory of logicHistory of mathematical logicHoward Jerome KeislerImage (mathematics)Inaccessible cardinalIndependence (mathematical logic)InferenceInfinite-valued logicInfinite setInformation theoryInhabited setInjective functionInterpretation (logic)Interpretation (model theory)Interpretation functionIntersection (set theory)IsomorphismJohn Newsome CrossleyJohn W. Dawson Jr.Kolmogorov complexityKripke's theory of truthKripke–Platek set theoryKőnig's lemmaLambda calculusLarge cardinalLeila HaaparantaLemma (mathematics)Leopold LöwenheimLindström'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 biconditionalLogical conjunctionLogical connectiveLogical consequenceLogical constantLogical disjunctionLogical equalityLogical equivalenceLogical truthLogicismLöwenheim numberMany-valued logicMap (mathematics)María ManzanoMatematicheskii SbornikMaterial conditionalMathWorldMathematical logicMathematical objectMathematische AnnalenMetalanguageMetalogicMetamathematicsMetatheoremMineola, New YorkMinimal axioms for Boolean algebraModel complete theoryModel theoryMonadic predicate calculusMonadic second-order logicMorse–Kelley set theoryNP (complexity)Naive set theoryNatural deductionNegationNew FoundationsNew York CityNon-Euclidean geometryNon-logical symbolNon-standard modelNon-standard model of arithmeticNonfirstorderizabilityOpen formulaOperation (mathematics)Ordinal analysisOrdinal numberOswald VeblenOxford University PressP (complexity)P versus NP problemParadoxes of set theoryPartial functionPartition of a setPeano axiomsPhilosophy of mathematicsPower setPreclosure operatorPredicate (mathematical logic)Predicate logicPredicate variablePrime modelPrimitive recursive arithmeticPrimitive recursive functionPrincipia MathematicaProof of impossibilityProof theoryPropositionPropositional calculusPropositional formulaPropositional variableQuantifier (logic)Quantifier rankReal closed fieldRecursionRecursive setRelation (mathematics)Relation algebraReverse mathematicsRobinson arithmeticRule of inferenceRussell's paradoxSatisfiabilitySaturated modelSchröder–Bernstein theoremSecond-order arithmeticSecond-order logicSelf-verifying theoriesSemantic theory of truthSemantics of logicSentence (mathematical logic)Sequent calculusSet (mathematics)Set theorySignature (logic)Singleton (mathematics)Skolem's paradoxSkolem arithmeticSkolem functionSkolem normal formSoundnessSpectrum of a sentenceSpectrum of a theorySpringer Science+Business MediaSquare of oppositionStanford Encyclopedia of PhilosophySteve Simpson (mathematician)Storrs, ConnecticutStrength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Supercompact cardinalSupertaskSurjective functionSyllogismSymbol (formal)Syntax (logic)T-schemaTarski's axiomatization of the realsTarski's axiomsTarski's theory of truthTarski's undefinability theoremTarski–Grothendieck set theoryTarski–Vaught testTautology (logic)Term (logic)Term logicThe Journal of Symbolic LogicTheoremTheories of truthTheory (mathematical logic)Thoralf SkolemThree-valued logicTimeline of mathematical logicTorontoTransactions of the American Mathematical SocietyTransfer principleTransitive setTrue arithmeticTruth predicateTruth tableTruth valueTuring machineType (model theory)Type theoryType–token distinctionUltrafilter (set theory)UltraproductUncountable setUndecidable problemUninterpreted functionUnion (set theory)Uniqueness quantificationUniversal quantificationUniversal setUniverse (mathematics)Up to isomorphismUrelementUse–mention distinctionValidity (logic)Variable (mathematics)Venn diagramVon Neumann universeVon Neumann–Bernays–Gödel set theoryWell-formed formulaWilfrid HodgesZermelo–Fraenkel set theory

139 concepts already in your glossary