# $\kappa $-categorical

Let $L$ be a first order language and let $S$ be a set of $L$-sentences^{}. If $\kappa $ is a cardinal, then $S$ is said to be if $S$ has a model of cardinality $\kappa $ and any two such models are isomorphic^{}.

In other words, $S$ is categorical iff it has a unique model of cardinality $\kappa $, to within isomorphism^{}.

Title | $\kappa $-categorical |
---|---|

Canonical name | kappacategorical |

Date of creation | 2013-03-22 13:00:33 |

Last modified on | 2013-03-22 13:00:33 |

Owner | Evandar (27) |

Last modified by | Evandar (27) |

Numerical id | 4 |

Author | Evandar (27) |

Entry type | Definition |

Classification | msc 03C35 |

Related topic | VaughtsTest |

Related topic | ExampleOfUniversalStructure |