### 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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