# syntactic compactness theorem for first order logic

Let $L$ be a first-order language, and $\mathrm{\Delta}\subseteq L$ be a set of sentences^{}. If $\mathrm{\Delta}$ is inconsistent, then some finite $\mathrm{\Gamma}\subseteq \mathrm{\Delta}$ is inconsistent.

Title | syntactic compactness theorem for first order logic |
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Canonical name | SyntacticCompactnessTheoremForFirstOrderLogic |

Date of creation | 2013-03-22 12:43:59 |

Last modified on | 2013-03-22 12:43:59 |

Owner | jihemme (316) |

Last modified by | jihemme (316) |

Numerical id | 5 |

Author | jihemme (316) |

Entry type | Theorem |

Classification | msc 03B10 |

Classification | msc 03C07 |

Related topic | UpwardsSkolemLowenheimTheorem |

Related topic | ProofOfUpwardsSkolemLowenheimTheorem |

Related topic | GettingModelsIModelsConstructedFromConstants |