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

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Abstract

We show that Kelley-Morse 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, it is relatively consistent with KM for any infinite λ with ω≤λ≤Ord that there is a class function F:Ord→λ that is not constant on any stationary class. Strikingly, 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.

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Original languageEnglish
Number of pages18
JournalFundamenta Mathematicae
Publication statusAccepted/In press - 10 Sep 2020
Peer-reviewedYes

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