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PreorderPartial orderPartial ordering relationStrict orderingTotal ordering relationWell-orderingWell-orderTransitive closureTotal orderQuasiorderEquivalence relationLinear orderPartially ordered setOrderPrecongruenceAlgebraic posetDirected setOrdered setOrdered fieldPrealgebraTotally ordered setRelationPosetLexicographic orderZermelo's theoremBinary relationEigenorderComplete latticePermutationFiltrationOrder typePretopologyLatticePregeometryUpper setElementary equivalenceOrdered ringGalois connectionPresburger arithmeticTransitivityLower setChainHeyting algebraBounded latticeTransfinite inductionCompleteness axiomTransitive setFrink idealPosheafπ-systemPredimensionIdealArithmetical setSemiorderOrdered pairPrequantizationAntichainCongruenceFilterPrenexSupersequencePresemifieldSuperbialgebraCorrespondenceHasse diagramPseudoalgebraCofinalitySecond-order logicSemilatticePluperfectionMajorizationShortlexAutotopismFunctionTrichotomyProperadPowerTransseriesPointclassLattice theoryPeano arithmeticPermutation groupPoincaré-birkhoff-witt theoremSupersetUnificationTopological sortSupremumPlücker relationOrder treeEquivalenceProfunctorPremaximalityPrimorialPremetricOrdinal numberDe morgan algebraPrime constellationKripke frameMultichainOrthocomplementation