Sh:569

• Shami, Z., & Shelah, S. (1999). Rigid \aleph_\epsilon-saturated models of superstable theories. Fund. Math., 162(1), 37–46. arXiv: math/9908158 MR: 1734816
• Abstract:
  We look naturally at models with: no two dimensions are equal, so if such a model is not rigid it has an automorphism (non trivial) then it maps every regular type to one not orthogonal to it; here comes the main point: if some \aleph_\epsilon saturated model of T has such an automorphism and NDOP then every one has an automorphism; by the analysis from [Sh 401] to be completed: this automorphism share this property, imitating [Sh-c X] also in other cardinlas there are rigid models even when teh model is not with all dimensions distinct (use levels of the tree decomposition); generally if T has an \aleph_\epsilon saturated rigid model then it is strongly deep (every type has depth infinity (enough has depth >0)) for them we have NDOP when one side comes from this type, then use a decomposion theorem with zero and two successors
• Version 1999-05-28_10 (13p) published version (10p)

@article{Sh:569,
 author = {Shami, Ziv and Shelah, Saharon},
 title = {{Rigid $\aleph_\epsilon$-saturated models of superstable theories}},
 journal = {Fund. Math.},
 fjournal = {Fundamenta Mathematicae},
 volume = {162},
 number = {1},
 year = {1999},
 pages = {37--46},
 issn = {0016-2736},
 mrnumber = {1734816},
 mrclass = {03C45},
 note = {\href{https://arxiv.org/abs/math/9908158}{arXiv: math/9908158}},
 arxiv_number = {math/9908158}
}