Supersimple ω-categorical groups and theories

Journal of Symbolic Logic 65 (2):767-776 (2000)
Abstract
An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl( $\emptyset$ )-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank
Keywords $\omega$-Categorical   Supersimple   Finite Rank   Group   Abelian   CM-Trivial
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DOI 10.2307/2586568
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References found in this work BETA
A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
ℵ0-Categorical, ℵ0-Stable Structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
Χo-Categorical, Χo-Stable Structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
From Stability to Simplicity.Byunghan Kim & Anand Pillay - 1998 - Bulletin of Symbolic Logic 4 (1):17-36.

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Citations of this work BETA
On Ω-Categorical, Generically Stable Groups and Rings.Jan Dobrowolski & Krzysztof Krupiński - 2013 - Annals of Pure and Applied Logic 164 (7-8):802-812.
CM-Triviality and Relational Structures.Viktor Verbovskiy & Ikuo Yoneda - 2003 - Annals of Pure and Applied Logic 122 (1-3):175-194.

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