Sh:509

• Shelah, S. (2008). Vive la différence. III. Israel J. Math., 166, 61–96. arXiv: math/0112237 DOI: 10.1007/s11856-008-1020-3 MR: 2430425
• Abstract:
  We show that, consistently, there is an ultrafilter {\mathcal F} on \omega such that if N^\ell_n=(P^\ell_n\cup Q^\ell_n, P^\ell_n,Q^\ell_n,R^\ell_n) (for \ell=1,2, n<\omega), P^\ell_n \cup Q^\ell_n \subseteq\omega, and \prod\limits_{n<\omega} N^1_n/ {\mathcal F}\equiv\prod\limits_{n<\omega}N^2_n/{\mathcal F} are models of the canonical theory t^{\rm ind} of the strong independence property, then every isomorphism from \prod\limits_{n<\omega} N^1_n/{\mathcal F} onto \prod\limits_{n< \omega} N^2_n/{\mathcal F} is a product isomorphism.
• Version 2006-06-19_11 (32p) published version (36p)

@article{Sh:509,
 author = {Shelah, Saharon},
 title = {{Vive la diff\'erence. III}},
 journal = {Israel J. Math.},
 fjournal = {Israel Journal of Mathematics},
 volume = {166},
 year = {2008},
 pages = {61--96},
 issn = {0021-2172},
 mrnumber = {2430425},
 mrclass = {03C20 (03E35)},
 doi = {10.1007/s11856-008-1020-3},
 note = {\href{https://arxiv.org/abs/math/0112237}{arXiv: math/0112237}},
 arxiv_number = {math/0112237}
}