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
Ehud Hrushovski (1993). A New Strongly Minimal Set. Annals of Pure and Applied Logic 62 (2):147-166.
John T. Baldwin & Niandong Shi (1996). Stable Generic Structures. Annals of Pure and Applied Logic 79 (1):1-35.
Ch Berline & D. Lascar (1986). Superstable Groups. Annals of Pure and Applied Logic 30 (1):1-43.
Kitty L. Holland (1997). Strongly Minimal Fusions of Vector Spaces. Annals of Pure and Applied Logic 83 (1):1-22.

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Citations of this work BETA
John T. Baldwin (2004). Notes on Quasiminimality and Excellence. Bulletin of Symbolic Logic 10 (3):334-366.

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