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- W2007682510 abstract "In this article, we introduce the notion of weakly measurable cardinal, a new large cardinal concept obtained by weakening the familiar concept of a measurable cardinal. Specifically, a cardinal κ is weakly measurable if for any collection documentclass{article}usepackage{amssymb}pagestyle{empty}begin{document}$mathcal {A}$end{document} containing at most κ+ many subsets of κ, there exists a nonprincipal κ-complete filter on κ measuring all sets in documentclass{article}usepackage{amssymb}pagestyle{empty}begin{document}$mathcal {A}$end{document}. Every measurable cardinal is weakly measurable, but a weakly measurable cardinal need not be measurable. Moreover, while the GCH cannot fail first at a measurable cardinal, I will show that it can fail first at a weakly measurable cardinal. More generally, if κ is measurable, then we can make its weak measurability indestructible by the forcing Add(κ, η) for any η while forcing the GCH to hold below κ. Nevertheless, I shall prove that weakly measurable cardinals and measurable cardinals are equiconsistent. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim" @default.
- W2007682510 created "2016-06-24" @default.
- W2007682510 creator A5020432951 @default.
- W2007682510 date "2011-04-05" @default.
- W2007682510 modified "2023-09-26" @default.
- W2007682510 title "Weakly measurable cardinals" @default.
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- W2007682510 doi "https://doi.org/10.1002/malq.201010006" @default.
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