# Sh:495

• Apter, A. W., & Shelah, S. (1997). On the strong equality between supercompactness and strong compactness. Trans. Amer. Math. Soc., 349(1), 103–128.
• Abstract:
We show that supercompactness and strong compactness can be equivalent even as properties of pairs of regular cardinals. Specifically, we show that if V \models ZFC + GCH is a given model (which in interesting cases contains instances of supercompactness), then there is some cardinal and cofinality preserving generic extension V[G]\models ZFC + GCH in which, (a) (preservation) for \kappa \le \lambda regular, if V \models \kappa is \lambda supercompact”, then V[G] \models \kappa is \lambda supercompact” and so that, (b) (equivalence) for \kappa \le \lambda regular, V[G] \models \kappa is \lambda strongly compact” iff V[G] \models \kappa is \lambda supercompact”, except possibly if \kappa is a measurable limit of cardinals which are \lambda supercompact.
• Version 1995-02-27_10 (49p) published version (26p)
Bib entry
@article{Sh:495,
author = {Apter, Arthur W. and Shelah, Saharon},
title = {{On the strong equality between supercompactness and strong compactness}},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {349},
number = {1},
year = {1997},
pages = {103--128},
issn = {0002-9947},
mrnumber = {1333385},
mrclass = {03E35 (03E55)},
doi = {10.1090/S0002-9947-97-01531-6},
note = {\href{https://arxiv.org/abs/math/9502232}{arXiv: math/9502232}},
arxiv_number = {math/9502232}
}