# 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. arXiv: math/9502232 DOI: 10.1090/S0002-9947-97-01531-6 MR: 1333385 -
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. - 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}, doi = {10.1090/S0002-9947-97-01531-6}, mrclass = {03E35 (03E55)}, mrnumber = {1333385}, mrreviewer = {A. Kanamori}, doi = {10.1090/S0002-9947-97-01531-6}, note = {\href{https://arxiv.org/abs/math/9502232}{arXiv: math/9502232}}, arxiv_number = {math/9502232} }