The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond

Volume 68 / 2020

Arthur W. Apter Bulletin Polish Acad. Sci. Math. 68 (2020), 1-10 MSC: 03E35, 03E55. DOI: 10.4064/ba180529-14-3 Published online: 3 April 2020


We construct via forcing a model for the level by level equivalence between strong compactness and supercompactness in which both $V = {\rm HOD}$ and the Ground Axiom (GA) are true. In our model, various versions of the combinatorial principles $\square $ and $\diamondsuit $ hold. In the model constructed, there are no restrictions on the class of supercompact cardinals.


  • 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.
    ORCID: 0000-0002-7091-3628

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