# finiteness of ${C}_{\cup}$ and ${C}_{\cap}$

###### Theorem 1

For any set $L$ and any subsets $X$ and $Y$ of $L$, the consequence operator ${C}_{\mathrm{\cap}}\mathit{}\mathrm{(}X\mathrm{,}Y\mathrm{)}$ is finitary.

###### Theorem 2

For any set $L$, any subsets $X$ of $L$, and any *finite* subset $Y$
of $L$, the consequence operator ${C}_{\mathrm{\cap}}\mathit{}\mathrm{(}X\mathrm{,}Y\mathrm{)}$ is finitary.

Title | finiteness of ${C}_{\cup}$ and ${C}_{\cap}$ |
---|---|

Canonical name | FinitenessOfCcupAndCcap |

Date of creation | 2013-03-22 16:30:04 |

Last modified on | 2013-03-22 16:30:04 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 4 |

Author | rspuzio (6075) |

Entry type | Theorem |

Classification | msc 03B22 |

Classification | msc 03G10 |

Classification | msc 03G25 |