Kelley-Morse set theory does not prove the class Fodor principle

Victoria Gitman, Joel David Hamkins, Asaf Karagila

Research output: Contribution to journalArticle

9 Downloads (Pure)

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 languageEnglish
Pages (from-to)133-154
Number of pages22
JournalFundamenta Mathematicae
Volume254
Issue number2
Early online date18 Feb 2021
DOIs
Publication statusPublished - 8 Apr 2021

Keywords

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

Cite this