Superrosy dependent groups having finitely satisfiable generics

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Annals of Pure and Applied Logic 151 (1):1-21 (2008)
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Abstract

We develop a basic theory of rosy groups and we study groups of small Uþ-rank satisfying NIP and having finitely satisfiable generics: Uþ-rank 1 implies that the group is abelian-by-finite, Uþ-rank 2 implies that the group is solvable-by-finite, Uþ-rank 2, and not being nilpotent-by-finite implies the existence of an interpretable algebraically closed field

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10.1016/j.apal.2007.09.004

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Citations of this work

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Stable types in rosy theories.Assaf Hasson & Alf Onshuus - 2010 - Journal of Symbolic Logic 75 (4):1211-1230.
On ω-categorical, generically stable groups.Jan Dobrowolski & Krzysztof Krupiński - 2012 - Journal of Symbolic Logic 77 (3):1047-1056.
Dimensional groups and fields.Frank O. Wagner - 2020 - Journal of Symbolic Logic 85 (3):918-936.

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References found in this work

Characterizing Rosy Theories.Clifton Ealy & Alf Onshuus - 2007 - Journal of Symbolic Logic 72 (3):919 - 940.
Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
One-dimensional groups over an o-minimal structure.Vladimir Razenj - 1991 - Annals of Pure and Applied Logic 53 (3):269-277.
Groups of dimension two and three over o-minimal structures.A. Nesin, A. Pillay & V. Razenj - 1991 - Annals of Pure and Applied Logic 53 (3):279-296.
Superstable fields and groups.G. Cherlin - 1980 - Annals of Mathematical Logic 18 (3):227.

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