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Axiom of choiceAxiom of regularityAxiom of infinityAxiom of unionCountable setAxiom of pairingAxiom of power setAxiom of extensionalityChoice functionCantor-bendixson theoremCompleteness axiomWell-orderUncountable setExtensionalityCantor's theoremAlgebraCountable additivityCardinalityIdealContinuum hypothesisFamilyπ-systemEquivalence classOrder typeZorn's lemmaOrdinal numberEquivalenceScott's trickAxiomatic systemPartitionGeneralized continuum hypothesisLimit cardinalBinary relationConnectionMatiyasevich's theoremRussell's paradoxOrderPowerCorrespondenceAxiom systemTransitive setUniversal setTeichmüller-tukey lemmaσ-additivityCartesian productLöwenheim-skolem theoremZermelo set theoryLindelöf covering theoremDirect productTransitive closureσ-algebraSet theorySperner's theoremClassPartially ordered setAx-kochen theoremInjectivityEmpty setPower setSetsPartial ordering relationQuotient setUnionNonexponentialityCategorical productDiagonal argumentCofinalityZermelo's theoremOrdered pairCartesian squareOrdered setGalileo's paradoxLinear orderTransfinite inductionLefschetz fixed-point theoremSylow theoremMaximalTotally ordered setArithmetical setQuasiorderAbsolute complementZermelo-fraenkel set theoryPropositionBijectionField axiomPigeonhole principleProofDouble countingSetoidCounting measureAleph numberPeano axiomInfinite seriesSet operationσ-finite measureCentral limit theoremWeakeningCofinite topologyAlgebraic posetArithmetical hierarchy