Type reduction and powerful types
\textit{M. Benda} [Fundam. Math. 81, 107-119 (1974; Zbl 0289.02038)] introduced the notion of a powerful type and proved that a theory \(T\) without a powerful type has an infinite number of non-isomorphic countable models. The author defines the notions of the reducibility of a theory over a type and a \(p\)-principal \(p\)-type. It is proved for a stable theory that there are no reducibilities over a non-principal powerful type. An example of a stable theory whose prime model over a realization of a powerful type \(p\) realizes a non-\(p\)-principal \(p\)-type is given.
scientific article; zbMATH DE number 59413