Supersimple $\omega$-categorical groups and theories

David M. Evans; Frank O. Wagner

doi:10.2307/2586568

Supersimple $\omega$-categorical groups and theories

David M. Evans, Frank O. Wagner

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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.

Original language	English
Pages (from-to)	767-776
Number of pages	10
Journal	Journal of Symbolic Logic
Volume	65
Issue number	2
DOIs	https://doi.org/10.2307/2586568
Publication status	Published - Jun 2000

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Cite this

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title = "Supersimple $\omega$-categorical groups and theories",

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({\o})-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.",

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