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2014 | 62 | 3 | 197-209
Tytuł artykułu

HOD-supercompactness, Indestructibility, and Level by Level Equivalence

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In an attempt to extend the property of being supercompact but not HOD-supercompact to a proper class of indestructibly supercompact cardinals, a theorem is discovered about a proper class of indestructibly supercompact cardinals which reveals a surprising incompatibility. However, it is still possible to force to get a model in which the property of being supercompact but not HOD-supercompact holds for the least supercompact cardinal κ₀, κ₀ is indestructibly supercompact, the strongly compact and supercompact cardinals coincide except at measurable limit points, and level by level equivalence between strong compactness and supercompactness holds above κ₀ but fails below κ₀. Additionally, we get the property of being supercompact but not HOD-supercompact at the least supercompact cardinal, in a model where level by level equivalence between strong compactness and supercompactness holds.
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  • Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.
  • The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, NY 10016, U.S.A.
  • Department of Mathematics and Computer Science, Kingsborough Community College-CUNY, 2001 Oriental Blvd, Brooklyn, NY 11235, U.S.A.
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bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-3-1
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