ascending chain condition

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

ascending chain condition is owned by anti zeus.

How to Cite This Entry

anti zeus. "ascending chain condition" (version 4). PlanetMath.org. Freely available at http://planetmath.org/AscendingChainCondition.html.

Classification

AMS MSC:

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

Pending Errata and Addenda

None. [ View all 5 ]

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