Martin’s axiom

For any cardinal $\kappa$, Martin’s Axiom for $\kappa$ ($M{A}_{\kappa }$) 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 $M{A}_{\kappa }$ holds for every .