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well-founded relation
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(Definition)
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A binary relation $R$ on a class $X$ is well-founded if and only if
- each nonempty subclass of $X$ contains an $R$ minimal element and,
- for each $x \in X$ $\lbrace y \mid y\,R\,x \rbrace$ is a set.
The notion of a well-founded relation is a generalization of that of a well-ordering relation: proof by induction and definition by recursion may be carried out over well-founded relations.
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"well-founded relation" is owned by ratboy. [ full author list (2) ]
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Cross-references: induction, proof, relation, well-ordering, contains, subclass, binary relation
There are 8 references to this entry.
This is version 6 of well-founded relation, born on 2007-07-18, modified 2008-04-01.
Object id is 9781, canonical name is WellFoundedRelation.
Accessed 1685 times total.
Classification:
| AMS MSC: | 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory ) |
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Pending Errata and Addenda
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