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Level by level equivalence and strong compactness

✍ Scribed by Arthur W. Apter

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
219 KB
Volume
50
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We force and construct models in which there are non‐supercompact strongly compact cardinals which aren't measurable limits of strongly compact cardinals and in which level by level equivalence between strong compactness and supercompactness holds non‐trivially except at strongly compact cardinals. In these models, every measurable cardinal κ which isn't either strongly compact or a witness to a certain phenomenon first discovered by Menas is such that for every regular cardinal λ > κ, κ is λ strongly compact iff κ is λ supercompact. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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