---
tag: H671WT55SK
kind: statement
role: lemma
name: Fodor's lemma for trees
sources:
  - wikipedia: en:1679022@r1350068977
    locator: Fodor's lemma
    note: adopted
    mention: wikipedia://en/1679022#MV7V
    sections: [Statement]
inventory: [F1JAH9ZZ16]
---

## Statement

For every non-special tree $T$ and regressive mapping $f:T\rightarrow T$ (that is, $f(t)<t$, with respect to the order on $T$, for every $t\in T$, $t\neq 0$), there is a non-special subtree $S\subseteq T$ on which $f$ is constant.