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  1. Ab initio generic structures which are superstable but not ω-stable.Koichiro Ikeda - 2012 - Archive for Mathematical Logic 51 (1):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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  • On generic structures with a strong amalgamation property.Koichiro Ikeda, Hirotaka Kikyo & Akito Tsuboi - 2009 - Journal of Symbolic Logic 74 (3):721-733.
    Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We (...)
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  • Stable generic structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
    Hrushovski originated the study of “flat” stable structures in constructing a new strongly minimal set and a stable 0-categorical pseudoplane. We exhibit a set of axioms which for collections of finite structure with dimension function δ give rise to stable generic models. In addition to the Hrushovski examples, this formalization includes Baldwin's almost strongly minimal non-Desarguesian projective plane and several others. We develop the new case where finite sets may have infinite closures with respect to the dimension function δ. In (...)
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  • A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
    We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.
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