Homogeneity in iterated models (Q1972817)

Iterated models are studied. The notion was introduced in the article ``Iterated extensions of models of countable theories and their applications'' by \textit{S.~S.~Goncharov} and \textit{M. Purmakhdian} [Algebra Logika 34, No. 6, 623-645 (1995; Zbl 0897.03033)]. An iterated model is a model in a signature expanded by predicate symbols for some types of its theory so that the sets of realizations of the types and the predicate symbols coincide correspondingly. The author describes a method of constructing iterated models with required properties. With the help of this method, two models are constructed: an iterated model whose theory has no standard homogeneous models (i.e. homogeneous iterated models of the same signature) and an iterated model with atomic theory that cannot be embedded into a standard homogeneous model.