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Model completeness of the new strongly minimal sets

Kitty L. Holland

Journal of Symbolic Logic 64 (3):946-962 (1999)

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Constructing ω-stable structures: model completeness.John T. Baldwin & Kitty Holland - 2004 - Annals of Pure and Applied Logic 125 (1-3):159-172.details 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’ (...) Download Export citation Bookmark 5 citations
Towards a finer classification of strongly minimal sets.John T. Baldwin & Viktor V. Verbovskiy - 2024 - Annals of Pure and Applied Logic 175 (2):103376.details Download Export citation Bookmark
Notes on quasiminimality and excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.details This paper ties together much of the model theory of the last 50 years. Shelah's attempts to generalize the Morley theorem beyond first order logic led to the notion of excellence, which is a key to the structure theory of uncountable models. The notion of Abstract Elementary Class arose naturally in attempting to prove the categoricity theorem for L ω 1 ,ω (Q). More recently, Zilber has attempted to identify canonical mathematical structures as those whose theory (in an appropriate logic) (...) Download Export citation Bookmark 3 citations
Raising to powers revisited.Boris Zilber - 2005 - Annals of Pure and Applied Logic 132 (1):67-95.details Download Export citation Bookmark 1 citation
Constructing ω-stable Structures: Rank k-fields.John T. Baldwin & Kitty Holland - 2003 - Notre Dame Journal of Formal Logic 44 (3):139-147.details Theorem: For every k, there is an expansion of the theory of algebraically closed fields (of any fixed characteristic) which is almost strongly minimal with Morley rank k. Download Export citation Bookmark
Model completeness of generic graphs in rational cases.Hirotaka Kikyo - 2018 - Archive for Mathematical Logic 57 (7-8):769-794.details Let \ be an ab initio amalgamation class with an unbounded increasing concave function f. We show that if the predimension function has a rational coefficient and f satisfies a certain assumption then the generic structure of \ has a model complete theory. Download Export citation Bookmark
Analytic Zariski structures and the Hrushovski construction.Nick Peatfield & Boris Zilber - 2005 - Annals of Pure and Applied Logic 132 (2):127-180.details A set of axioms is presented defining an ‘analytic Zariski structure’, as a generalisation of Hrushovski and Zilber’s Zariski structures. Some consequences of the axioms are explored. A simple example of a structure constructed using Hrushovski’s method of free amalgamation is shown to be a non-trivial example of an analytic Zariski structure. A number of ‘quasi-analytic’ results are derived for this example e.g. analogues of Chow’s theorem and the proper mapping theorem. Download Export citation Bookmark 3 citations
An Analytic Zariski Structure Over a Field.Nick Peatfield - 2006 - Archive for Mathematical Logic 45 (6):739-768.details Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms. Download Export citation Bookmark

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