# descending chain condition

A partially ordered set $S$ (for example, a collection of subsets of a set $X$, ordered by inclusion) satisfies the 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).

Title descending chain condition DescendingChainCondition 2013-03-22 12:01:14 2013-03-22 12:01:14 antizeus (11) antizeus (11) 7 antizeus (11) Definition msc 06A99 DCC