# partitions less than cofinality

If $$ then $\kappa \to {(\kappa )}_{\lambda}^{1}$.

This follows easily from the definition of cofinality. For any coloring^{} $f:\kappa \to \lambda $ then define $g:\lambda \to \kappa +1$ by $g(\alpha )=|{f}^{-1}(\alpha )|$. Then $$, and by the normal rules of cardinal arithmetic $$. Since $$, there must be some $$ such that $g(\alpha )=\kappa $.

Title | partitions less than cofinality |
---|---|

Canonical name | PartitionsLessThanCofinality |

Date of creation | 2013-03-22 12:55:56 |

Last modified on | 2013-03-22 12:55:56 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 6 |

Author | Henry (455) |

Entry type | Result |

Classification | msc 03E04 |

Related topic | Arrowsrelation |

Related topic | ArrowsRelation |