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ExtensionalityAxiom of unionAxiom of pairingAxiom of choiceAxiom of regularityAxiom of infinityAxiom of power setAxiom of countable choiceCompleteness axiomAbsolute complementElementary equivalenceEquivalence relationAxiomatic systemCardinalityZermelo set theoryCantor-bendixson theoremTransitive setSetoidContinuum hypothesisSupersetBinary relationSet theoryConservative extensionUniversal setAxiom systemTransitive closureSet-theoretic differenceZorn's lemmaIntersectionEquivalence classSymmetric differenceGeneralized continuum hypothesisLaw of identityCountable setSetsEquivalenceRussell's paradoxPower setZermelo-fraenkel set theoryBijectionSet operationOrder typeEmpty setWell-orderCartesian squareTotal orderAlgebraZermelo's theoremCompletenessCartesian productCantor's theoremComplementMaximalUnionCorrespondencePowerRelative complementOrderArithmetical setScott's trickCountable additivityOrdered pairIdealLinear orderElementGeneralizationExtensionDirect productSperner's theoremField axiomsConnectionTransfinite inductionForcingClassPartial ordering relationOrdinal numberEquisatisfiabilityAleph-onePeano axiomGödel's incompleteness theoremPrinciple of explosionPerfect setAutoequivalencePartitionSecond-order logicField axiomMatiyasevich's theoremNull setTotally ordered setMonotonicitySingleton setSimple extensionLöwenheim-skolem theoremSingletonDirected setRelationEquationEquivalence of categoriesKan extensionNormal extension