Linked from

The 28 pages that link to Partial order, each with the reason it gives.

• Equivalence relationCompared with: A partial order replaces symmetry with antisymmetry, allowing distinct elements to be comparable without being equivalent.

• Binary relationBroader topic: It represents comparisons that need not make every pair comparable.

• Transitive relationBroader topic: Transitivity helps make chains of comparisons consistent in partially ordered sets.

• Well-founded relationRelated: Many familiar well-founded relations are partial orders, though well-foundedness does not require one.

• Reflexive relationBroader topic: Reflexivity makes every object comparable to itself in the order.

• Topological sortingNarrower topic: A DAG’s reachability relation defines precedence constraints that a topological order extends.

• Total orderCompared with: A partial order lacks the comparability requirement that distinguishes total orders.

• Strict partial orderCompared with: It expresses the non-strict counterpart through reflexive comparisons.

• Filtration (probability theory)Related: Set inclusion orders the sigma-algebras in a filtration from less to more information.

• Least elementNarrower topic: Leastness is defined relative to the relation ordering the set.

• PreorderCompared with: Adding antisymmetry to a preorder produces a partial order.

• Antisymmetric relationBroader topic: Antisymmetry is one of the three defining conditions of a partial order.

• Forcing (mathematics)Related: Forcing conditions are ordered by strength, with stronger conditions carrying more information.

• Hasse diagramNarrower topic: The underlying relation determines which elements are comparable in the diagram.

• Symmetric relationCompared with: Partial orders use antisymmetry, which is distinct from the symmetry defined here.

• Maximal elementRelated: Its comparisons decide whether any element lies strictly above a candidate.

• Minimal elementRelated: Its comparison relation determines whether any element lies strictly below a candidate.

• Sorting algorithmRelated: Some sortable data have incomparable elements, complicating the meaning of a fully ordered result.

• Upper boundNarrower topic: Upper bounds are defined relative to an order, which need not compare every pair of elements.

• Equality relationCompared with: A partial order shares reflexivity and transitivity but generally is not symmetric.

• Order theoryBroader topic: This relation allows some elements to remain incomparable.

• Dilworth's theoremRelated: Comparability under this relation determines membership in chains and antichains.

• Kleene fixed-point theoremNarrower topic: The theorem compares approximations using an order rather than numerical distance.

• Turing degreeRelated: Turing degrees form an ordered structure under reducibility, though not a linear order.

• Connected relationCompared with: Partial orders permit incomparable pairs, whereas connected relations do not.

• Infimum and supremumNarrower topic: Infima and suprema are defined relative to an order, which need not compare every pair.

• Kruskal's tree theoremNarrower topic: Well-quasi-orders generalize partial orders by permitting distinct elements to be equivalent.

• Rasiowa–Sikorski lemmaRelated: The lemma applies to sets whose elements are ordered by a partial order.