# inductively ordered

A partially ordered set^{} $A$ is inductively ordered iff every chain of elements of $A$ has an upper bound in $A$.

Examples. The power set^{} ${2}^{M}$ of any set $M$ is inductively ordered by the set inclusion (http://planetmath.org/Set); any finite set^{} of integers is inductively ordered by divisibility.

Cf. inductive set^{}.

Title | inductively ordered |
---|---|

Canonical name | InductivelyOrdered |

Date of creation | 2013-03-22 14:55:21 |

Last modified on | 2013-03-22 14:55:21 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 8 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 06A99 |

Related topic | ZornsLemma |

Defines | inductive order |

Defines | inductively orderes set |