The consistency of level by level equivalence with V=HOD, the Ground Axiom, and instances of square and diamond

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

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).