Linked from

The 16 pages that link to Well-founded relation, each with the reason it gives.

• RecursionRelated: A recursive procedure terminates when each call descends through a well-founded measure.

• Well-ordering theoremRelated: Well-orders are well-founded, though well-founded relations need not be linear.

• Axiom of dependent choiceCompared with: A serial relation on a nonempty set cannot be well-founded, since it always permits another successor.

• Recursive definitionRelated: A well-founded dependency prevents recursive clauses from descending forever.

• Axiom of FoundationNarrower topic: Membership on sets satisfies this structural condition under Foundation.

• Transfinite recursionRelated: Well-foundedness generalizes the absence of endlessly earlier stages that supports recursive definitions.

• Maximal elementCompared with: Well-foundedness guarantees minimal elements, the downward analogue rather than maximal elements.

• Minimal elementRelated: Well-foundedness guarantees minimal elements for every nonempty region of the ordered set.

• Membership relationRelated: The axiom of foundation requires membership to be well-founded in standard Zermelo-Fraenkel set theory.

• Ordinal analysisRelated: Ordinal analyses often measure which well-foundedness claims a theory can establish.

• Transfinite inductionRelated: Ordinals are well-founded, enabling induction beyond the natural numbers.

• Infinite regressCompared with: Well-foundedness rules out the descending dependency chains that generate many regresses.

• Axiom of regularityRelated: Regularity says membership is well-founded on every set.

• Well-orderRelated: Well-foundedness supplies the subset-minimum condition; adding totality yields a well-order.

• Kruskal's tree theoremRelated: Minimal-counterexample arguments rely on well-foundedness to choose a smallest obstruction.

• Mostowski collapse lemmaRelated: Well-foundedness makes the recursive definition of the collapse map terminate.