We construct two models containing exactly one supercompact cardinal in which all nonsupercompact measurable cardinals are strictly taller than they are either strongly compact or supercompact. In the flrst of these models, level by level equivalence between strong compactness and supercompactness holds. In the other, level by level inequivalence between strong compactness and supercompactness holds. Each universe has only one strongly compact cardinal and contains relatively few large cardinals.
['Arthur W. Apter']
Tallness and level by level equivalence and inequivalence