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descending chain condition (Definition)

A partially ordered set $S$ (for example, a collection of subsets of a set $X$ ordered by inclusion) satisfies the descending chain condition or DCC if there does not exist an infinite descending chain $s_1 > s_2 > \cdots$ of elements of $S$

See also the ascending chain condition (ACC).




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Other names:  DCC
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Cross-references: ascending chain condition, chain, infinite, inclusion, subsets, collection, partially ordered set
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This is version 3 of descending chain condition, born on 2001-11-23, modified 2004-05-01.
Object id is 984, canonical name is DescendingChainCondition.
Accessed 4624 times total.

Classification:
AMS MSC06A99 (Order, lattices, ordered algebraic structures :: Ordered sets :: Miscellaneous)

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