We prove two theorems concerning strong compactness, measurability, and the class of supercompact cardinals. We begin by showing, relative to the appropriate hypotheses, that it is consistent non-trivially for every supercompact cardinal to be the limit of (non-supercompact) strongly compact cardinals. We then show, relative to the existence of a non-trivial (proper or improper) class of supercompact cardinals, that it is possible to have a model with the same class of supercompact cardinals in which every measurable cardinal δ is strongly compact.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-5,
author = {Arthur W. Apter},
title = {Strong compactness, measurability, and the class of supercompact cardinals},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {65-78},
zbl = {0981.03053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-5}
}
Arthur W. Apter. Strong compactness, measurability, and the class of supercompact cardinals. Fundamenta Mathematicae, Tome 167 (2001) pp. 65-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-5/