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chain condition
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(Definition)
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A partial order $P$ satisfies the $\kappa$ chain condition if for any $S\subseteq P$ with $|S|=\kappa$ then there exist distinct $x,y\in S$ and some $p$ such that $p\leq x$ and $p\leq y$
If $\kappa=\aleph_1$ then $P$ is said to satisfy the countable chain condition (c.c.c.)
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"chain condition" is owned by Henry.
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Cross-references: satisfies, partial order
There are 10 references to this entry.
This is version 4 of chain condition, born on 2002-07-30, modified 2006-06-23.
Object id is 3241, canonical name is ChainCondition.
Accessed 8953 times total.
Classification:
| AMS MSC: | 03E35 (Mathematical logic and foundations :: Set theory :: Consistency and independence results) |
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Pending Errata and Addenda
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