Coordinatization in Superstable Theories. II

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1988Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 307, page 411 (issn: 0002-9947,

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Authors: Buechler, Steven;

doi: 10.2307/2000771 , 10.1090/s0002-9947-1988-0936825-2

Coordinatization in Superstable Theories. II

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Abstract

In this paper we prove Theorem A. Suppose that T T is superstable and U ( a / A ) = α + 1 U(a/A) = \alpha + 1 , for some α \alpha . Then in T eq {T^{{\text {eq}}}} there is a c ∈ acl ⁡ ( A a ) ∖ acl ⁡ ( A ) c \in \operatorname {acl} (Aa)\backslash \operatorname {acl} (A) such that one of the following holds. (i) U ( c / A ) = 1 U(c/A) = 1 . (ii) stp ⁡ ( c / A ) \operatorname {stp} (c/A) has finite Morley rank. In fact, this strong type is semiminimal with respect to a strongly minimal set.

Related Organizations

University of Wisconsin–Milwaukee
United States

Keywords

Classification theory, stability, and related concepts in model theory, superstable theory, strongly minimal set, finite Morley rank

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