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SupremumExtensionalityAxiom of choiceComplete latticeField axiomAxiom of extensionalityAxiom of infinityAxiom of unionZorn's lemmaField axiomsWell-orderArchimedean ordered fieldUpper setLexicographic orderTotal orderAlgebraic posetAxiom of countable choiceEssential supremumOrdered fieldGödel's incompleteness theoremCompletenessAxiom of pairingAxiom of power setZermelo's theoremLatticeAxiom of regularityComplete measureInfimumCofinalityLinear orderTotal ordering relationCompositumIdealUpper limitMaximumSuperextensionOrdered setMaxtermMaximalOrder typeTotally ordered setPresemifieldContinuum hypothesisAbsolute complementOuter measurePartial orderTranscendence degreePeano axiomLower setWell-orderingCompletionAx-kochen theoremOrderSpecializationShortlexDirected setAutotopismμ-completionPremaximalityLim supPartial ordering relationClosureArithmetic combinatoricsBounded latticeBinary relationOrdered ringAxiom systemOrdinal numberAxiomatic systemPartially ordered setNormal extensionSupersetMonotonicityEssential infimumLöwenheim-skolem theoremRobinson arithmeticChainStrict orderingCantor's theoremSupersequenceUltrafilterTransfinite inductionFrink idealCharacteristicFreiman's theoremAlgebraic closureClosed intervalLindelöf covering theoremCantor-bendixson theoremSupersolutionArithmetical setTeichmüller-tukey lemmaArchimedean propertyAntichainAlgebraCommutator lengthMaximal idealTopological spaceBicompletionPrewellordering