Kelley–Morse set theory does not prove the class Fodor principle
Victoria Gitman, Joel David Hamkins, Asaf Karagila · Fundamenta Mathematicae · 2021
We show that Kelley–Morse KM set theory does not prove the class Fodor principle, the assertion that every regressive class function $F:S\to {\rm Ord}$ defined on a stationary class $S$ is constant on a stationary subclass. Indeed, for every $\omega \leq