# 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 $$.

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 |