Journal of Symbolic Logic 65 (1):371-391 (2000)

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Abstract
We provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from 'primitive extensions' to the natural numbers a theory T μ of an expansion of an algebraically closed field which has Morley rank 2. Finally, we show that if μ is not finite-to-one the theory may not be ω-stable
Keywords finite rank expansion   algebraically closed fields   model completeness
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DOI 10.2307/2586544
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References found in this work BETA

A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Superstable Groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
Stable Generic Structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
Superstable Fields and Groups.G. Cherlin - 1980 - Annals of Mathematical Logic 18 (3):227.

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Citations of this work BETA

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Notes on Quasiminimality and Excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.
The Additive Collapse.Andreas Baudisch - 2009 - Journal of Mathematical Logic 9 (2):241-284.

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