Definition
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie as the foundation for a modern treatment of Euclidean geometry. Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff.
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MooreEdward Vermilye HuntingtonElement (mathematics)Elementary diagramElementary equivalenceElementary function arithmeticEmpty setEncyclopedia of MathematicsEnumerationEquiconsistencyEquivalence relationEuclid's ElementsEuclidean geometryEuclidean plane geometryEuclidean spaceEuropean Mathematical SocietyExistential 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 theoryGilbert de Beauregard RobinsonGrothendieck universeGround expressionGround formulaGrundlagen der GeometrieGödel's completeness theoremGödel's incompleteness theoremsGödel numberingHalting problemHenri PoincaréHenry George ForderHereditary setHigher-order logicHilbert systemHistory of logicHistory of mathematical logicHoward EvesImage (mathematics)Inaccessible cardinalIndependence (mathematical logic)InferenceInfinite-valued logicInfinite setInformation theoryInhabited setInjective functionInterpretation (logic)Interpretation (model theory)Interpretation functionIntersection (set theory)IsomorphismIvor Grattan-GuinnessKolmogorov complexityKripke's theory of truthKripke–Platek set theoryLambda calculusLarge cardinalLemma (mathematics)LibriVoxLindström's theoremLine (geometry)List 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–Skolem theoremMany-valued logicMap (mathematics)Mario PieriMaterial conditionalMathematical logicMathematical objectMetalanguageMetamathematicsMinimal axioms for Boolean algebraModel complete theoryModel theoryMonadic predicate calculusMonadic second-order logicMoritz PaschMorse–Kelley set theoryNP (complexity)Naive set theoryNatural deductionNegationNew FoundationsNon-Euclidean geometryNon-logical symbolNon-standard modelNon-standard model of arithmeticOpen formulaOperation (mathematics)Ordinal analysisOrdinal numberOswald VeblenP (complexity)P versus NP problemParadoxes of set theoryPartition of a setPasch's axiomPasch's theoremPeano axiomsPhilosophy of mathematicsPlane (mathematics)Playfair's axiomPoint (geometry)Power setPredicate (mathematical logic)Predicate logicPredicate variablePrime modelPrimitive notionPrimitive recursive arithmeticPrimitive recursive functionPrincipia MathematicaProof of impossibilityProof theoryPropositionPropositional calculusPropositional formulaPropositional variableQuantifier (logic)Quantifier rankR. 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