# oligomorphic permutation group

A permutation group^{} acting on a countably
infinite^{} set is called *oligomorphic*,
if it has finitely many orbits of $n$-tuples,
for all $n\ge 1$.

Ryll-Nardzewski, Engeler, and Svenonius proved that
a countably infinite first-order structure^{} has an oligomorphic
automorphism group if and only if the structure is
$\omega $-categorical.

Title | oligomorphic permutation group |
---|---|

Canonical name | OligomorphicPermutationGroup |

Date of creation | 2013-03-22 15:15:36 |

Last modified on | 2013-03-22 15:15:36 |

Owner | amador (8479) |

Last modified by | amador (8479) |

Numerical id | 6 |

Author | amador (8479) |

Entry type | Definition |

Classification | msc 03C35 |

Related topic | CountablyCategoricalStructures |

Defines | oligomorphic automorphism group |