Journal of Symbolic Logic

Supersimple $\omega$-Categorical Groups and Theories

David M. Evans and Frank O. Wagner

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Abstract

An $\omega$-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 $\omega$-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple $\omega$-categorical CM-trivial theory has finite SU-rank.

Article information

Source
J. Symbolic Logic, Volume 65, Issue 2 (2000), 767-776.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746076

Mathematical Reviews number (MathSciNet)
MR1771084

Zentralblatt MATH identifier
0965.03050

JSTOR
links.jstor.org

Subjects
Primary: 03C45: Classification theory, stability and related concepts [See also 03C48]

Keywords
$\omega$-Categorical Supersimple Finite Rank Group Abelian CM-Trivial

Citation

Evans, David M.; Wagner, Frank O. Supersimple $\omega$-Categorical Groups and Theories. J. Symbolic Logic 65 (2000), no. 2, 767--776. https://projecteuclid.org/euclid.jsl/1183746076


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