# 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 MartinsAxiom 2013-03-22 12:54:55 2013-03-22 12:54:55 Henry (455) Henry (455) 6 Henry (455) Definition msc 03E50 MA