# upward Lowenheim-Skolem theorem

Let $L$ be a first-order language and let $\mathcal{A}$ be an infinite^{} $L$-structure^{}. Then if $\kappa $ is a cardinal with $\kappa \ge \mathrm{Max}(|\mathcal{A}|,|L|)$ then there is an $L$-structure $\mathcal{B}$ such that $|\mathcal{B}|=\kappa $ and $\mathcal{A}\preccurlyeq \mathcal{B}$.

Title | upward Lowenheim-Skolem theorem |
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Canonical name | UpwardLowenheimSkolemTheorem |

Date of creation | 2013-03-22 13:00:39 |

Last modified on | 2013-03-22 13:00:39 |

Owner | Evandar (27) |

Last modified by | Evandar (27) |

Numerical id | 6 |

Author | Evandar (27) |

Entry type | Theorem |

Classification | msc 03C07 |