Classification and interpretation

Journal of Symbolic Logic 54 (1):138-159 (1989)
Abstract
Let S and T be countable complete theories. We assume that T is superstable without the dimensional order property, and S is interpretable in T in such a way that every model of S is coded in a model of T. We show that S does not have the dimensional order property, and we discuss the question of whether $\operatorname{Depth}(S) \leq \operatorname{Depth}(T)$ . For Mekler's uniform interpretation of arbitrary theories S of finite similarity type into suitable theories T s of groups we show that $\operatorname{Depth}(S) \leq \operatorname{Depth}(T_S) \leq 1 + \operatorname{Depth}(S)$
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DOI 10.2307/2275021
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References found in this work BETA
Superstable Groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
The Number of Uncountable Models of Ω-Stable Theories.Jürgen Saffe - 1983 - Annals of Pure and Applied Logic 24 (3):231-261.

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Citations of this work BETA
Mekler's Construction Preserves CM-Triviality.Andreas Baudisch - 2002 - Annals of Pure and Applied Logic 115 (1-3):115-173.

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