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 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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 19 Nov 2020 00:47
Last Modified: 03 May 2021 23:40
URI: https://ueaeprints.uea.ac.uk/id/eprint/77730
DOI: 10.4064/fm725-9-2020

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