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- Publisher
- Springer Journals
- Copyright
- Copyright © 2003 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-003-0181-3
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we first prove several general theorems about strongness, supercompactness, and indestructibility, along the way giving some new applications of Hamkins’ lottery preparation forcing to indestructibility. We then show that it is consistent, relative to the existence of cardinals κ<λ so that κ is λ supercompact and λ is inaccessible, for the least strongly compact cardinal κ to be the least strong cardinal and to have its strongness, but not its strong compactness, indestructible under κ-strategically closed forcing.
Journal
Archive for Mathematical Logic – Springer Journals
Published: May 16, 2003