# chain condition

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.)

Title chain condition ChainCondition 2013-03-22 12:53:38 2013-03-22 12:53:38 Henry (455) Henry (455) 7 Henry (455) Definition msc 03E35 PartialOrder PartialOrderWithChainConditionDoesNotCollapseCardinals chain condition countable chain condition $\kappa$-chain condition c.c.c. ccc