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

Gitman, Victoria, Hamkins, Joel David and Karagila, Asaf (2021) Kelley-Morse set theory does not prove the class Fodor principle. Fundamenta Mathematicae, 254 (2). pp. 133-154. ISSN 0016-2736

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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.

Item Type: Article
Uncontrolled Keywords: class forcing,fodor's lemma,kelley-morse set theory,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 19 Nov 2020 00:47
Last Modified: 22 Jul 2021 00:00
URI: https://ueaeprints.uea.ac.uk/id/eprint/77730
DOI: 10.4064/fm725-9-2020

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