# universal structure

Let $L$ be a first order language, and let $R$ be an elementary class of $L$-structures^{}.
Let $\kappa $ be a cardinal. ${R}_{\kappa}$ be the set of structures from $R$ with cardinality less than or equal to $\kappa $.

Let $M\in {R}_{\kappa}$.
Suppose that for every $N\in {R}_{\kappa}$ there is an embedding^{} of $N$ into $M$.
Then we say $M$ is universal^{}.

Title | universal structure |
---|---|

Canonical name | UniversalStructure |

Date of creation | 2013-03-22 13:23:09 |

Last modified on | 2013-03-22 13:23:09 |

Owner | Timmy (1414) |

Last modified by | Timmy (1414) |

Numerical id | 4 |

Author | Timmy (1414) |

Entry type | Definition |

Classification | msc 03C50 |

Classification | msc 03C52 |

Defines | universal |