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

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Gitman, Victoria, Hamkins, Joel David and Karagila, Asaf ORCID: https://orcid.org/0000-0003-1289-0904 (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
UEA Research Groups:	Faculty of Science > Research Groups > Logic
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/1904.04190
Depositing User:	LivePure Connector
Date Deposited:	19 Nov 2020 00:47
Last Modified:	21 Oct 2022 22:35
URI:	https://ueaeprints.uea.ac.uk/id/eprint/77730
DOI:	10.4064/fm725-9-2020

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