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 $p\le x$ and $p\le y$.

If $\kappa ={\mathrm{\aleph }}_1$ then $P$ is said to satisfy the countable chain condition (c.c.c.)