descending chain condition
DescendingChainCondition
2001-11-23 21:23:26
2004-05-01 14:40:30
Definition
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A partially ordered set $S$ (for example, a collection of subsets of a set $X$, ordered by inclusion) satisfies the {\it descending chain condition} or {\it 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).