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Indestructibility under adding Cohen subsets and level by level equivalence

✍ Scribed by Arthur W. Apter

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 120 KB
Volume: 55
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200810006

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✦ Synopsis

Abstract

We construct a model for the level by level equivalence between strong compactness and supercompactness in which the least supercompact cardinal κ has its strong compactness indestructible under adding arbitrarily many Cohen subsets. There are no restrictions on the large cardinal structure of our model (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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If κ < λ are such that κ is indestructibly supercompact and λ is 2 λ supercompact, it is known from [4] that {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ violates level by level equivalence between strong compactness and supercompactness} must be unbounded i