Inaccessible Cardinals, Failures of GCH, and Level-by-Level Equivalence

We construct models for the level by level equivalence between strong compactness and supercompactness containing failures of GCH at inaccessible cardinals. In one of these models, no cardinal is supercompact up to an inaccessible cardinal, and for every inaccessible cardinal δ, 2δ > δ++. In another of these models, no cardinal is supercompact up to an inaccessible cardinal, and the only inaccessible cardinals at which GCH holds are also measurable. These results extend and generalize [1, Theorem 3].