Order, lattices, ordered algebraic structures Well-orders, well-founded orders, well-quasi-orders Concept
Well-founded order
Summary
A well-founded order is a partial order in which every nonempty subset has a minimal element. Equivalently, assuming the axiom of dependent choice, there is no infinite strictly decreasing sequence. It is the order case of a well-founded relation. It is exactly what is needed for proofs by well-founded induction and definitions by well-founded recursion. A well-order is a well-founded order that is also total.
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| Tag | 55WD0H03CZ |
|---|---|
| URI | m2://55WD0H03CZ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A06, 03E20 |
| Specializes | Well-founded relation |
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