We show that universal indestructibility for both strong compactness and supercompactness is consistent with the existence of two strongly compact cardinals. This is in contrast to the fact that if κ is supercompact and universal indestructibility for either strong compactness or supercompactness holds, then no cardinal λ > κ is measurable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-2,
author = {Arthur W. Apter},
title = {Universal Indestructibility is Consistent with Two Strongly Compact Cardinals},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {131-135},
zbl = {1112.03045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-2}
}
Arthur W. Apter. Universal Indestructibility is Consistent with Two Strongly Compact Cardinals. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 131-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-2/