The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond
Volume 68 / 2020
Bulletin Polish Acad. Sci. Math. 68 (2020), 1-10
MSC: 03E35, 03E55.
DOI: 10.4064/ba180529-14-3
Published online: 3 April 2020
Abstract
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.
