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 |
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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: | |
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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