Constructing ω-stable structures: Rank 2 fields

Journal of Symbolic Logic 65 (1):371-391 (2000)
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.
Stable Generic Structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
Superstable Groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
Strongly Minimal Fusions of Vector Spaces.Kitty L. Holland - 1997 - Annals of Pure and Applied Logic 83 (1):1-22.

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Citations of this work BETA
Constructing Ω-Stable Structures: Model Completeness.John T. Baldwin & Kitty Holland - 2004 - Annals of Pure and Applied Logic 125 (1-3):159-172.
Notes on Quasiminimality and Excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.

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