The consistency of level by level equivalence with , 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.
