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Field axiomField theoryPresemifieldArchimedean ordered fieldCompleteness axiomAlgebraic number fieldOrdered fieldAlgebraic structureQuadratic fieldNumber fieldField of scalarsQuasifieldFixed fieldAxiom systemScalar fieldField extensionPerfect fieldSemifieldAxiomatic systemExtensionalityField lineNormal extensionGalois fieldField of quotientsFundamental theoremDegreeAxiom of choiceAxiom of infinityArmstrong's axiomsAxial pointTheoryAxiom of extensionalityDomainAxisFieldlineNullstellensatzForcingExtension fieldTopological fieldLinear formAxial vectorSpecializationSchematic variableDefinitionPrime fieldPolynomial basisPeano axiomCharacteristicAx-grothendieck theoremAbsolute geometryAxiom of unionDomain theoryProofSubjectTrivial absolute valueAxiom of power setOne-formAxiom of regularityAlgebraic closureField of fractionsStructuralismAxoidAlgebraic number theoryAbstract algebraSimple extensionFormal logicX-axisVector fieldDimensionAbsolute formFree boolean algebraFinite geometryAlgebraic extensionClosed formInitial objectSplitting fieldGalois theoryCoordinate axisRedexScalar functionJordan algebraMathematical structureArithmetical setPropositionFunctionMathematical realismCovectorFormalismLogicismLinear algebraRoot of unitySystem of equationsAx-kochen theoremProjective geometryPropositional calculusUniversal algebraAlgebra over a fieldAxiom of countable choiceGeneralizationSet theory