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  1. Equivalence Relations Which Are Borel Somewhere.William Chan - 2017 - Journal of Symbolic Logic 82 (3):893-930.
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  • Level by Level Inequivalence Beyond Measurability.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (7-8):707-712.
    We construct models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In each model, above the supercompact cardinal, there are finitely many strongly compact cardinals, and the strongly compact and measurable cardinals precisely coincide.
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  • 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.
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