Archive for Mathematical Logic 47 (2):101-110 (2008)

Abstract
If κ < λ are such that κ is indestructibly supercompact and λ is measurable, then we show that both A = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries the maximal number of normal measures} and B = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries fewer than the maximal number of normal measures} are unbounded in κ. The two aforementioned phenomena, however, need not occur in a universe with an indestructibly supercompact cardinal and sufficiently few large cardinals. In particular, we show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must carry fewer than the maximal number of normal measures. We also, however, show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must carry the maximal number of normal measures. If we weaken the requirements on indestructibility, then this last result can be improved to obtain a model with an indestructibly supercompact cardinal κ in which every measurable cardinal δ < κ carries the maximal number of normal measures
Keywords Supercompact cardinal  Measurable cardinal  Normal measure  Indestructibility
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DOI 10.1007/s00153-008-0079-1
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References found in this work BETA

Gap Forcing: Generalizing the Lévy-Solovay Theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Possible Behaviours for the Mitchell Ordering.James Cummings - 1993 - Annals of Pure and Applied Logic 65 (2):107-123.

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Citations of this work BETA

Indestructibility and Stationary Reflection.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):228-236.
Indestructibility, HOD, and the Ground Axiom.Arthur W. Apter - 2011 - Mathematical Logic Quarterly 57 (3):261-265.
Indestructibility and Destructible Measurable Cardinals.Arthur W. Apter - 2016 - Archive for Mathematical Logic 55 (1-2):3-18.

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