# proof of compactness theorem for first order logic

The theorem states that if a set of sentences^{} of a first-order language $L$ is inconsistent, then some finite subset of it is inconsistent. Suppose $\mathrm{\Delta}\subseteq L$ is inconsistent. Then by definition $\mathrm{\Delta}\u22a2\u27c2$, i.e. there is a formal proof of “false” using only assumptions^{} from $\mathrm{\Delta}$. Formal proofs are finite objects, so let $\mathrm{\Gamma}$ collect all the formulas^{} of $\mathrm{\Delta}$ that are used in the proof.

Title | proof of compactness theorem for first order logic |
---|---|

Canonical name | ProofOfCompactnessTheoremForFirstOrderLogic |

Date of creation | 2013-03-22 12:44:02 |

Last modified on | 2013-03-22 12:44:02 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 4 |

Author | CWoo (3771) |

Entry type | Proof |

Classification | msc 03B10 |

Classification | msc 03C07 |