# Fodor’s lemma

If $\kappa $ is a regular^{}, uncountable cardinal, $S$ is a stationary subset of $\kappa $, and $f:\kappa \to \kappa $ is regressive on $S$ (that is, $$ for any $\alpha \in S$) then there is some $\gamma $ and some stationary ${S}_{0}\subseteq S$ such that $f(\alpha )=\gamma $ for any $\alpha \in {S}_{0}$.

Title | Fodor’s lemma |
---|---|

Canonical name | FodorsLemma |

Date of creation | 2013-03-22 12:53:14 |

Last modified on | 2013-03-22 12:53:14 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 4 |

Author | Henry (455) |

Entry type | Theorem |

Classification | msc 03E10 |

Synonym | pushing down lemma |

Related topic | Stationary |

Defines | Fodor’s lemma |