PlanetMath: descending chain condition

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descending chain condition

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A partially ordered set (for example, a collection of subsets of a set , 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 .

"descending chain condition" is owned by antizeus.

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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 3668 times total.

Classification:

06A99 (Order, lattices, ordered algebraic structures :: Ordered sets :: Miscellaneous)

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