Linked from

The 34 pages that link to Ordinal number, each with the reason it gives.

• John von NeumannNarrower topic: His set-based definition of ordinals became a standard way to represent them.

• IntegerCompared with: Ordinals generalize counting order, while integers measure signed quantity.

• Set theoryRelated: Ordinals formalize transfinite sequences and support recursive definitions.

• Natural numberRelated: Natural numbers can name finite positions as well as quantities.

• Zermelo–Fraenkel set theoryNarrower topic: Ordinals extend the set-theoretic construction of natural numbers to transfinite orders.

• Georg CantorRelated: Cantor developed transfinite ordinals to describe positions beyond every finite number.

• Continuum hypothesisRelated: The cardinal aleph-one is defined using the least uncountable ordinal.

• CardinalityCompared with: Ordinals encode order structure, while cardinalities ignore the arrangement of elements.

• Well-ordering theoremBroader topic: Every well-order has an ordinal as its order type.

• Well-founded relationRelated: Ordinals provide canonical well-founded orders for measuring stages and ranks.

• Cumulative hierarchyRelated: Ordinals index the stages, including successor steps and limit stages.

• Total orderRelated: Ordinals are compared by a canonical total order that reflects their order types.

• Axiom of unionRelated: For a limit ordinal, union combines all earlier ordinals into that ordinal.

• Cardinal numberCompared with: Ordinals encode order, while cardinals encode size without regard to arrangement.

• Gödel's constructible universeRelated: Ordinals index the stages of L, including its limit stages.

• InfinityRelated: Ordinals extend counting to infinite orderings, unlike cardinal numbers, which measure size.

• Transfinite recursionNarrower topic: Ordinals index the stages of the recursion and distinguish successor stages from limits.

• Chain (order theory)Related: Well-ordered chains provide the order types represented by ordinals.

• Axiom of constructibilityRelated: The stages of L are indexed by ordinals, continuing through the entire ordinal class.

• Axiom of infinityNarrower topic: The natural numbers can be represented as the least infinite ordinal.

• Felix HausdorffRelated: Hausdorff studied ordinal arithmetic and transfinite order types.

• Goodstein's theoremRelated: Replacing each sequence term's base with omega yields a strictly descending ordinal measure.

• Ordinal analysisNarrower topic: Transfinite ordinals are the measures at the heart of the method.

• Transfinite inductionNarrower topic: Transfinite induction ranges over ordinal positions, including infinite stages.

• Order theoryRelated: Ordinals classify well-orders up to order isomorphism.

• Von Neumann universeNarrower topic: Ordinals name the stages at which the cumulative hierarchy grows.

• Von Neumann–Bernays–Gödel set theoryRelated: The class of all ordinals is a proper class in NBG, not a set.

• Number (mathematics)Related: Ordinals capture position and ordering, a role distinct from measuring quantity.

• Aleph numberRelated: Ordinal indices specify which aleph appears in the sequence.

• Well-orderNarrower topic: Ordinals classify well-orders up to order-preserving bijection.

• Erdős–Rado theoremRelated: Ordinal-indexed notation distinguishes the finite-subset sizes in partition relations.

• Axiom of limitation of sizeRelated: Ordinals index the cumulative hierarchy and help formalize the universe of sets.

• Fodor's lemmaNarrower topic: Regressiveness depends on ordinal order, and the theorem's cardinal domain is itself an ordinal.

• Mostowski collapse lemmaRelated: The collapse identifies well-founded extensional linear orders with ordinal membership structures.