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OrderOrdinal numberWell-orderTotal orderTotally ordered setLinear orderPartially ordered setEquivalence classPosetPartial orderOrdered pairPartial ordering relationQuasiorderOrdered fieldOrdered ringPreorderBinary relationAlgebraic posetSortOrdered setChainAntichainTotal ordering relationRelationSetoidSet theoryStrict orderingClassAxiom of choiceUpper setTypeZermelo's theoremGalois connectionTransitive closureDomain theoryEquivalence relationLexicographic orderWell-orderingCorrespondenceMonotone functionLatticeCardinalityQuotient setPermutationDirected setSet operationTrichotomyOrder treeScott's trickBounded latticeSetsType theoryCongruenceLower setEquivalenceTosetAxiom of pairingBijectionPointclassPowerEigenorderAxiom of regularityIdealLimit ordinalSemiorderOperator theorySet-builder notationFiltrationCountable setCompleteness axiomAxiom of extensionalityCongruence classGroup actionAxiom of countable choicePower setAxiom of unionConjugacy classCategory theoryPrewellorderingTopological sortHomotopy theoryExtensionalityCantor-bendixson theoremCosetElementSupremumZorn's lemmaArithmetical setAlgebraPartitionSupersetShortlexCharacteristicSecond-order logicAutomorphism groupElementary equivalenceAleph numberArithmetical hierarchyAlgebraic structureTransitive set