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Singular Failures of GCH and Level by Level Equivalence

Volume 62 / 2014

Arthur W. Apter Bulletin Polish Acad. Sci. Math. 62 (2014), 11-21 MSC: 03E35, 03E55. DOI: 10.4064/ba62-1-2


We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal $\kappa $, there is an unbounded set of singular cardinals which witness the only failures of GCH in the universe. In this model, the structure of the class of supercompact cardinals can be arbitrary.


  • Arthur W. ApterDepartment 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.

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