# 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 |