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 $\alpha \in S_0$.