# Sh:569

• Shami, Z., & Shelah, S. (1999). Rigid \aleph_\epsilon-saturated models of superstable theories. Fund. Math., 162(1), 37–46.
• 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
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}
}