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Indestructibility under adding Cohen subsets and level by level equivalence |
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| Authors: | Arthur W Apter |
| Institution: | 1. Department of Mathematics, Baruch College of CUNY, New York, New York 10010, USA;2. The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, New York 10016, USA |
| Abstract: | We construct a model for the level by level equivalence between strong compactness and supercompactness in which the least supercompact cardinal κ has its strong compactness indestructible under adding arbitrarily many Cohen subsets. There are no restrictions on the large cardinal structure of our model (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
| Keywords: | Supercompact cardinal strongly compact cardinal strong cardinal indestructibility Gitik iteration of Prikry‐like forcings level by level equivalence between strong compactness and supercompactness |