Martin’s axiom

For any cardinal $\kappa$ , Martin’s Axiom for $\kappa$ ( $MA_{\kappa}$ ) states that if $P$ is a partial order satisfying ccc then given any set of $\kappa$ dense (http://planetmath.org/DenseInAPoset) subsets of $P$ , there is a directed (http://planetmath.org/DirectedSet) subset intersecting each such subset. Martin’s Axiom states that $MA_{\kappa}$ holds for every $\kappa<2^{\aleph_{0}}$ .

Title	Martin’s axiom
Canonical name	MartinsAxiom
Date of creation	2013-03-22 12:54:55
Last modified on	2013-03-22 12:54:55
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	6
Author	Henry (455)
Entry type	Definition
Classification	msc 03E50
Defines	MA