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Strongly minimal groups in the theory of compact complex spaces. (English) Zbl 1103.03038
From a paper by B. Zilber [“Model theory and algebraic geometry”, in: M. Weese et al. (eds.), Proceedings of the tenth easter conference on model theory, Wendisch Rietz, Germany, April 12–17, 1993. Berlin: Humboldt-Universität, Fachbereich Mathematik, Humboldt-Univ. Berlin, Sekt. Math., Semin.-ber. 93-1, 202–222 (1993; Zbl 0796.03040)] it follows that the key to a model-theoretic structure theory for sets definable in compact complex manifolds is a description of the interpretable strongly minimal groups.
A. Pillay and T. Scanlon [Trans. Am. Math. Soc. 355, No. 10, 3843–3859 (2003; Zbl 1021.03025)] described these groups but left open the question of what strongly minimal groups might be definable in elementary extensions of compact complex manifolds.
In the present paper the authors complete the classification.

MSC:
03C60 Model-theoretic algebra
20A15 Applications of logic to group theory
32C15 Complex spaces
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