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.)

Title	chain condition
Canonical name	ChainCondition
Date of creation	2013-03-22 12:53:38
Last modified on	2013-03-22 12:53:38
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	7
Author	Henry (455)
Entry type	Definition
Classification	msc 03E35
Related topic	PartialOrder
Related topic	PartialOrderWithChainConditionDoesNotCollapseCardinals
Defines	chain condition
Defines	countable chain condition
Defines	$\kappa$-chain condition
Defines	c.c.c.
Defines	ccc