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HOD-supercompactness, Indestructibility, and Level by Level Equivalence

Tom 62 / 2014

Arthur W. Apter, Shoshana Friedman Bulletin Polish Acad. Sci. Math. 62 (2014), 197-209 MSC: 03E35, 03E55. DOI: 10.4064/ba62-3-1

Streszczenie

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 $\kappa _0$, $\kappa _0$ 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 $\kappa _0$ but fails below $\kappa _0$. 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.

Autorzy

  • Arthur W. ApterDepartment of Mathematics
    Baruch College of CUNY
    New York, NY 10010, U.S.A.
    and
    The CUNY Graduate Center, Mathematics
    365 Fifth Avenue
    New York, NY 10016, U.S.A.
    e-mail
  • Shoshana FriedmanDepartment of Mathematics and Computer Science
    Kingsborough Community College-CUNY
    2001 Oriental Blvd, Brooklyn, NY 11235, U.S.A.
    e-mail

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