On the non-extendibility of strongness and supercompactness through strong compactness
Arthur W. Apter (2002)
Fundamenta Mathematicae
Similarity:
If κ is either supercompact or strong and δ < κ is α strong or α supercompact for every α < κ, then it is known δ must be (fully) strong or supercompact. We show this is not necessarily the case if κ is strongly compact.