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Universal partial indestructibility and strong compactness
Author(s) -
Apter Arthur W.
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200510004
Subject(s) - mathematics , compact space , regular cardinal , forcing (mathematics) , pure mathematics , rank (graph theory) , construct (python library) , combinatorics , discrete mathematics , mathematical analysis , computer science , programming language
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)