On the non-extendibility of strongness and supercompactness through strong compactness
Volume 174 / 2002
Fundamenta Mathematicae 174 (2002), 87-96
MSC: 03E35, 03E55.
DOI: 10.4064/fm174-1-5
Abstract
If $\kappa $ is either supercompact or strong and $\delta < \kappa $ is $\alpha $ strong or $\alpha $ supercompact for every $\alpha < \kappa $, then it is known $\delta $ must be (fully) strong or supercompact. We show this is not necessarily the case if $\kappa $ is strongly compact.
