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  1. On the consistency strength of level by level inequivalence.Arthur W. Apter - 2017 - Archive for Mathematical Logic 56 (7-8):715-723.
    We show that the theories “ZFC \ There is a supercompact cardinal” and “ZFC \ There is a supercompact cardinal \ Level by level inequivalence between strong compactness and supercompactness holds” are equiconsistent.
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  • Precisely controlling level by level behavior.Arthur W. Apter - 2017 - Mathematical Logic Quarterly 63 (1-2):77-84.
    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 ‐supercompact, where is the least inaccessible cardinal greater than κ.
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