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Le Carre de l'egalite

Journal of Symbolic Logic 64 (3):1339-1355 (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
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

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