Constructing ω-stable structures: model completeness

Annals of Pure and Applied Logic 125 (1-3):159-172 (2004)
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Abstract

The projective plane of Baldwin 695) is model complete in a language with additional constant symbols. The infinite rank bicolored field of Poizat 1339) is not model complete. The finite rank bicolored fields of Baldwin and Holland 371; Notre Dame J. Formal Logic , to appear) are model complete. More generally, the finite rank expansions of a strongly minimal set obtained by adding a ‘random’ unary predicate are almost strongly minimal and model complete provided the strongly minimal set is ‘well-behaved’ and admits ‘exactly rank k formulas’. The last notion is a geometric condition on strongly minimal sets formalized in this paper

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Citations of this work

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References found in this work

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.
On Model-Completeness.Per Lindström - 1964 - Theoria 30 (3):183-196.
Constructing ω-stable structures: Rank 2 fields.John T. Baldwin & Kitty Holland - 2000 - Journal of Symbolic Logic 65 (1):371-391.
Model completeness of the new strongly minimal sets.Kitty Holland - 1999 - Journal of Symbolic Logic 64 (3):946-962.

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