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