ascending chain condition AscendingChainCondition 2001-11-23 21:16:06 2004-05-01 14:40:12 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A partially ordered set $S$ (for example, a collection of subsets of a set $X$ when ordered by inclusion) satisfies the {\it ascending chain condition} or {\it ACC} if there does not exist an infinite ascending chain $s_1 < s_2 < \cdots$ of elements of $S$. See also the descending chain condition (DCC).