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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-rankOther Versions
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Citations of this work
Omega-Categorical Pseudofinite Groups.Dugald Macpherson & Katrin Tent - forthcoming - Journal of Symbolic Logic:1-14.
Applications of the group configuration theorem in simple theories.Ivan Tomašić & Frank O. Wagner - 2003 - Journal of Mathematical Logic 3 (02):239-255.
Definable nilpotent and soluble envelopes in groups without the independence property.Ricardo de Aldama - 2013 - Mathematical Logic Quarterly 59 (3):201-205.
CM-triviality and relational structures.Viktor Verbovskiy & Ikuo Yoneda - 2003 - Annals of Pure and Applied Logic 122 (1-3):175-194.
The group configuration in simple theories and its applications.Itay Ben-Yaacov, Ivan Toma{\V. S.}I.{\'C. & Frank Wagner - 2002 - Bulletin of Symbolic Logic 8 (2):283-298.
References found in this work
A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
ℵ0-Categorical, ℵ0-stable structures.Gregory Cherlin, Leo Harrington & Alistair 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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