# 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)

Bib entry

@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} }