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Supersimple ω-categorical groups and theories

Published online by Cambridge University Press:  12 March 2014

David M. Evans  and
Frank O. Wagner
David M. Evans
Affiliation:
School of Mathematics, UEA, Norwich NR4 7TJ, UK, E-mail: d.evans@uea.ac.uk
Frank O. Wagner*
Affiliation:
Mathematical Institute, University of Oxford, 24–29 ST Giles' Oxford Ox1 3LB., UK
*
Current address: Institut Girard Desargues, Université Claude Bernard, Mathématiques, bâtiment, 101, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne-cedex, France, E-mail: wagner@maths.ox.ac.uk, E-mail: wagner@desargues.univ-lyonl.fr
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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(ø)-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

ω-categoricalsupersimplefinite rankgroupabelianCM-trivial
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 767 - 776
Copyright
Copyright © Association for Symbolic Logic 2000

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