Interpreting groups inside modular strongly minimal homogeneous models

Journal of Mathematical Logic 3 (01):127-142 (2003)
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Abstract

A large homogeneous model M is strongly minimal, if any definable subset is either bounded or has bounded complement. In this case is a pregeometry, where bcl denotes the bounded closure operation. In this paper, we show that if M is a large homogeneous strongly minimal structure and is non-trivial and locally modular, then M interprets a group. In addition, we give a description of such groups.

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10.1142/s0219061303000200

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References found in this work

Strong splitting in stable homogeneous models.Tapani Hyttinen & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):201-228.
Minimale Gruppen.Joachim Reineke - 1975 - Mathematical Logic Quarterly 21 (1):357-359.
Almost orthogonal regular types.Ehud Hrushovski - 1989 - Annals of Pure and Applied Logic 45 (2):139-155.
Canonical Finite Diagrams and Quantifier Elimination.Tapani Hyttinen - 2002 - Mathematical Logic Quarterly 48 (4):533-554.

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