## Abstract

We show that Kelley-Morse KM set theory does not prove the class Fodor principle, the assertion that every regressive class function F : S → Ord defined on a stationary class S is constant on a stationary subclass. Indeed, for every ω ≤ λ ≤ Ord, it is relatively consistent with KM that there is a class function F : Ord → λ that is not constant on any stationary class, and moreover λ is the least ordinal for which such a counterexample function exists. As a corollary of this result, it is consistent with KM that there is a class A ⊆ ω × Ord such that each section An = {α| (n,α) ∈ A} contains a class club, but nAn is empty. Consequently, it is relatively consistent with KM that the class club filter is not σ-closed.

Original language | English |
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Pages (from-to) | 133-154 |

Number of pages | 22 |

Journal | Fundamenta Mathematicae |

Volume | 254 |

Issue number | 2 |

Early online date | 18 Feb 2021 |

DOIs | |

Publication status | Published - 8 Apr 2021 |

## Keywords

- Class forcing
- Fodor's lemma
- Kelley-Morse set theory