# 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. - Current version: 2012-12-17_10 (32p) published version (32p)

Bib entry

@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}, mrclass = {03C55 (03C45 03C68 03E40)}, mrnumber = {2563810}, mrreviewer = {O. V. Belegradek}, note = {\href{https://arxiv.org/abs/math/0703477}{arXiv: math/0703477}}, arxiv_number = {math/0703477} }