Universal partial indestructibility and strong compactness

✍ Scribed by Arthur W. Apter

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 153 KB
• Volume: 51
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200510004

✦ Synopsis

Abstract

For any ordinal δ, let λ~δ~ be the least inaccessible cardinal above δ. We force and construct a model in which the least supercompact cardinal κ is indestructible under κ‐directed closed forcing and in which every measurable cardinal δ < κ is < λ~δ~ strongly compact and has its < λ~δ~ strong compactness indestructible under δ‐directed closed forcing of rank less than λ~δ~. In this model, κ is also the least strongly compact cardinal. We also establish versions of this result in which κ is the least strongly compact cardinal but is not supercompact. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)