Abstract
We show that KelleyMorse 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 σclosed.
Original language  English 

Pages (fromto)  133154 
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
 KelleyMorse set theory
Profiles

Asaf Karagila
 School of Mathematics  UKRI Future Leaders Fellow
 Logic  Member
Person: Research Group Member, Academic, Teaching & Research