On some questions concerning strong compactness |
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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, USA 2. The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, NY, 10016, USA
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Abstract: | A question of Woodin asks if κ is strongly compact and GCH holds below κ, then must GCH hold everywhere? One variant of this question asks if κ is strongly compact and GCH fails at every regular cardinal δ?< κ, then must GCH fail at some regular cardinal δ?≥ κ? Another variant asks if it is possible for GCH to fail at every limit cardinal less than or equal to a strongly compact cardinal κ. We get a negative answer to the first of these questions and positive answers to the second of these questions for a supercompact cardinal κ in the context of the absence of the full Axiom of Choice. |
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