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.
• Version 1995-02-27_10 (49p) published version (26p)

@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}
}