# countably categorical structures

A countably infinite^{} structure^{} is called *countably categorical* (also called *$\omega $-categorical*, or *${\mathrm{\aleph}}_{\mathrm{0}}$-categorical*)
if all countable^{} models of its first-order theory are isomorphic^{}.

Ryll-Nardzewski, Engeler, and Svenonius proved that a countable structure is $\omega $-categorical if and only if it has an oligomorphic automorphism group.

Title | countably categorical structures |
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Canonical name | CountablyCategoricalStructures |

Date of creation | 2013-03-22 15:15:38 |

Last modified on | 2013-03-22 15:15:38 |

Owner | amador (8479) |

Last modified by | amador (8479) |

Numerical id | 5 |

Author | amador (8479) |

Entry type | Derivation |

Classification | msc 03C35 |

Synonym | ${\mathrm{\aleph}}_{0}$-categorical |

Synonym | $\omega $-categorical |

Related topic | oligomorphicPermutationGroup |

Related topic | OligomorphicPermutationGroup |