Sh:897

• Shelah, S. (2008). Theories with Ehrenfeucht-Fraïssé equivalent non-isomorphic models. Tbil. Math. J., 1, 133–164. arXiv: math/0703477 MR: 2563810
• Abstract:
  Our “large scale” aim is to characterize the first order T (at least the countable ones) such that: for every ordinal \alpha there \lambda,M_1,M_2 such that M_1,M_2 are non-isomorphic models of T of cardinality \lambda which are EF_{\alpha,\lambda}-equivalent. We expect that as in the main gap ([Sh:c,XII]) we get a strong dichotomy, so in the non-structure side we have more, better example, and in the structure side we have a parallel of [Sh:c,XIII]. We presently prove the consistency of the non-structure side for T which is \aleph_0-independent (= not strongly dependent) or just not strongly stable, even for PC(T_1,T) and more for unstable T (see [Sh:c,VII] or [Sh:h]) and infinite linear order I.
• Version 2012-12-17_12 (32p) published version (32p)

@article{Sh:897,
 author = {Shelah, Saharon},
 title = {{Theories with Ehrenfeucht-Fra\"iss\'e equivalent non-isomorphic models}},
 journal = {Tbil. Math. J.},
 fjournal = {Tbilisi Mathematical Journal},
 volume = {1},
 year = {2008},
 pages = {133--164},
 issn = {1875-158X},
 mrnumber = {2563810},
 mrclass = {03C55 (03C45 03C68 03E40)},
 note = {\href{https://arxiv.org/abs/math/0703477}{arXiv: math/0703477}},
 arxiv_number = {math/0703477}
}