Type reduction and powerful types
type: Item
instance of: scholarly article
title: Type reduction and powerful types
zbMATH Open document ID: 0781.03017
DOI: 10.1007/BF00972944
published in: Siberian Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03C15
Mathematics Subject Classification ID: 03C35
zbMATH DE Number: 59413
zbMATH Keywords: powerful type
zbMATH Keywords: countable models
zbMATH Keywords: reducibility of a theory over a type
zbMATH Keywords: \(p\)-principal \(p\)-type
zbMATH Keywords: stable theory
zbMATH Keywords: prime model
author: S. V. Sudoplatov
MaRDI profile type: Publication
cites work: Remarks on countable models
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description: scientific article; zbMATH DE number 59413