# compactness

A logic is said to be $(\kappa ,\lambda )$-compact, if the following holds

If $\mathrm{\Phi}$ is a set of sentences

^{}of cardinality less than or equal to $\kappa $ and all subsets of $\mathrm{\Phi}$ of cardinality less than $\lambda $ are consistent, then $\mathrm{\Phi}$ is consistent.

For example, first order logic is $(\omega ,\omega )$-compact, for if all finite subsets of some class of sentences are consistent, so is the class itself.

Title | compactness |
---|---|

Canonical name | Compactness |

Date of creation | 2013-03-22 13:49:34 |

Last modified on | 2013-03-22 13:49:34 |

Owner | Aatu (2569) |

Last modified by | Aatu (2569) |

Numerical id | 5 |

Author | Aatu (2569) |

Entry type | Definition |

Classification | msc 03B99 |

Defines | compactness |