# homogeneous

Let $L$ be a first order language. Let $M$ be an $L$-structure^{}.
Then we say $M$ is homogeneous^{} if the following holds:

if$\sigma $ is an isomorphism^{} between finite substructures of $M$,
then $\sigma $ extends to an automorphism^{} of $M$.

Title | homogeneous |
---|---|

Canonical name | Homogeneous |

Date of creation | 2013-03-22 13:23:13 |

Last modified on | 2013-03-22 13:23:13 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 5 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 03C50 |

Related topic | ExampleOfUniversalStructure |

Related topic | RandomGraph |