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  1. Finite and Infinite Model Theory-A Historical Perspective.John Baldwin - 2000 - Logic Journal of the IGPL 8 (5):605-628.
    We describe the progress of model theory in the last half century from the standpoint of how finite model theory might develop.
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  • Notes on Quasiminimality and Excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.
    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) (...)
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  • Strongly Minimal Fusions of Vector Spaces.Kitty L. Holland - 1997 - Annals of Pure and Applied Logic 83 (1):1-22.
    We provide a simple and transparent construction of Hrushovski's strongly minimal fusions in the case where the fused strongly minimal sets are vector spaces. We strengthen Hrushovski's result by showing that the strongly minimal fusions are model complete.
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  • CM-Triviality and Relational Structures.Viktor Verbovskiy & Ikuo Yoneda - 2003 - Annals of Pure and Applied Logic 122 (1-3):175-194.
    Continuing work of Baldwin and Shi 1), we study non-ω-saturated generic structures of the ab initio Hrushovski construction with amalgamation over closed sets. We show that they are CM-trivial with weak elimination of imaginaries. Our main tool is a new characterization of non-forking in these theories.
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  • Ab Initio Generic Structures Which Are Superstable but Not Ω-Stable.Koichiro Ikeda - 2012 - Archive for Mathematical Logic 51 (1-2):203-211.
    Let L be a countable relational language. Baldwin asked whether there is an ab initio generic L-structure which is superstable but not ω-stable. We give a positive answer to his question, and prove that there is no ab initio generic L-structure which is superstable but not ω-stable, if L is finite and the generic is saturated.
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  • A Note on Stability Spectrum of Generic Structures.Yuki Anbo & Koichiro Ikeda - 2010 - Mathematical Logic Quarterly 56 (3):257-261.
    We show that if a class K of finite relational structures is closed under quasi-substructures, then there is no saturated K-generic structure that is superstable but not ω -stable.
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