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Constructing ω-stable structures: rank 2 fields

Published online by Cambridge University Press:  12 March 2014

John T. Baldwin  and
Kitty Holland
John T. Baldwin
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinoisat Chicago, 851 S. Morgan St., Chicago, IL 60607, USA, E-mail: [email protected]
Kitty Holland
Affiliation:
Department of Mathematics, Northern Illinois University, Dekalb, IL 60115, USA, E-mail: [email protected]
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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 Tμ 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 371 - 391
Copyright
Copyright © Association for Symbolic Logic 2000

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