Indestructible strong compactness and level by level inequivalence |
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Authors: | Arthur W Apter |
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Institution: | 1. Department of Mathematics, Baruch College of CUNY, , New York, NY 10010 United States of America;2. CUNY Graduate Center, , New York, NY 10016 United States of America |
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Abstract: | If are such that δ is indestructibly supercompact and γ is measurable, then it must be the case that level by level inequivalence between strong compactness and supercompactness fails. We prove a theorem which points to this result being best possible. Specifically, we show that relative to the existence of cardinals such that κ1 is λ‐supercompact and λ is inaccessible, there is a model for level by level inequivalence between strong compactness and supercompactness containing a supercompact cardinal in which κ’s strong compactness, but not supercompactness, is indestructible under κ‐directed closed forcing. In this model, κ is the least strongly compact cardinal, and no cardinal is supercompact up to an inaccessible cardinal. |
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Keywords: | Supercompact cardinal strongly compact cardinal Mahlo cardinal indestructibility level by level inequivalence between strong compactness and supercompactness Př í krý forcing Př í krý sequence non‐reflecting stationary set of ordinals lottery sum 03E35 03E55 |
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