Coordinatization in superstable theories. II

Buechler, Steven

doi:10.1090/S0002-9947-1988-0936825-2

Coordinatization in superstable theories. II
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by Steven Buechler

Trans. Amer. Math. Soc. 307 (1988), 411-417

DOI: https://doi.org/10.1090/S0002-9947-1988-0936825-2

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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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Contributions to stable model theory