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Precisely controlling level by level behavior
Abstract:We construct four models containing one supercompact cardinal in which level by level equivalence between strong compactness and supercompactness and level by level inequivalence between strong compactness and supercompactness are precisely controlled at each non‐supercompact measurable cardinal. In these models, no cardinal κ is urn:x-wiley:09425616:media:malq201500018:malq201500018-math-0001‐supercompact, where urn:x-wiley:09425616:media:malq201500018:malq201500018-math-0002 is the least inaccessible cardinal greater than κ.
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