# Fodor’s lemma

If $\kappa$ is a regular, uncountable cardinal, $S$ is a stationary subset of $\kappa$, and $f:\kappa\rightarrow\kappa$ is regressive on $S$ (that is, $f(\alpha)<\alpha$ 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 FodorsLemma 2013-03-22 12:53:14 2013-03-22 12:53:14 Henry (455) Henry (455) 4 Henry (455) Theorem msc 03E10 pushing down lemma Stationary Fodor’s lemma