Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence

✍ Scribed by Arthur W. Apter

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 125 KB
• Volume: 52
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200610005

✦ Synopsis

Abstract

We construct models for the level by level equivalence between strong compactness and supercompactness in which for κ the least supercompact cardinal and δ ≤ κ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2^δ^ > δ ^+^ and δ is < 2^δ^ supercompact. In these models, the structure of the class of supercompact cardinals can be arbitrary, and the size of the power set of κ can essentially be made as large as desired. This extends and generalizes [5, Theorem 2] and [4, Theorem 4]. We also sketch how our techniques can be used to establish a weak indestructibility result. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)