Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Coordinatization in superstable theories. II


Author: Steven Buechler
Journal: Trans. Amer. Math. Soc. 307 (1988), 411-417
MSC: Primary 03C45
MathSciNet review: 936825
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Abstract: In this paper we prove

Theorem A. Suppose that $ T$ is superstable and $ U(a/A) = \alpha + 1$, for some $ \alpha $. Then in $ {T^{{\text{eq}}}}$ there is a $ c \in \operatorname{acl} (Aa)\backslash \operatorname{acl} (A)$ such that one of the following holds.

(i) $ U(c/A) = 1$.

(ii) $ \operatorname{stp} (c/A)$ has finite Morley rank. In fact, this strong type is semiminimal with respect to a strongly minimal set.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0936825-2
Article copyright: © Copyright 1988 American Mathematical Society