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 languageEnglish
Pages (from-to)767-776
Number of pages10
JournalJournal of Symbolic Logic
Volume65
Issue number2
DOIs
Publication statusPublished - Jun 2000

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