Rigid $\aleph_\epsilon$--saturated models of superstable theories

by Shami and Shelah. [SzSh:569]
Fundamenta Math, 199
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

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