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

Apter Arthur W.

Bulletin of the Polish Academy of Sciences. Mathematics

2020

Vol. 68, no. 1

1--10

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.