PlanetMath: ascending chain condition

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ascending chain condition

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

"ascending chain condition" is owned by antizeus.

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Other names:

ACC

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Cross-references: descending chain condition, chain, infinite, inclusion, subsets, collection, partially ordered set
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This is version 4 of ascending chain condition, born on 2001-11-23, modified 2004-05-01.
Object id is 982, canonical name is AscendingChainCondition.
Accessed 4706 times total.

Classification:

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

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