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Classification and interpretation

Published online by Cambridge University Press:  12 March 2014

Andreas Baudisch
Andreas Baudisch*
Affiliation:
Institut für Mathematik, Akademie der Wissenschaften der DDR, 1086 Berlin, East Germany
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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 Depth(S) ≤ Depth(T). For Mekler's uniform interpretation of arbitrary theories S of finite similarity type into suitable theories TS of groups we show that Depth(S) ≤ Depth(TS) ≤ 1 + Depth(S).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 1 , March 1989 , pp. 138 - 159
Copyright
Copyright © Association for Symbolic Logic 1989

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References

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