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  1. Unidimensional theories are superstable.Katsuya Eda - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.
    A first order theory T of power λ is called unidimensional if any twoλ+-saturated models of T of the same cardinality are isomorphic. We prove here that such theories are superstable, solving a problem of Shelah. The proof involves an existence theorem and a definability theorem for definable groups in stable theories, and an analysis of their relation to regular types.
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  • A dichotomy theorem for regular types.Ehud Hrushovski & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 45 (2):157-169.
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  • Unidimensional theories are superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-138.
    A first order theory T of power λ is called unidimensional if any twoλ+-saturated models of T of the same cardinality are isomorphic. We prove here that such theories are superstable, solving a problem of Shelah. The proof involves an existence theorem and a definability theorem for definable groups in stable theories, and an analysis of their relation to regular types.
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  • Trivial pursuit: Remarks on the main gap.John T. Baldwin & Leo Harrington - 1987 - Annals of Pure and Applied Logic 34 (3):209-230.
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  • Locally modular theories of finite rank.Steven Buechler - 1986 - Annals of Pure and Applied Logic 30 (1):83-94.
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  • Meager forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.
    T is stable. We define the notion of meager regular type and prove that a meager regular type is locally modular. Assuming I < 2o and G is a definable abelian group with locally modular regular generics, we prove a counterpart of Saffe's conjecture. Using these results, for superstable T we prove the conjecture of vanishing multiplicities. Also, as a further application, in some additional cases we prove a conjecture regarding topological stability of pseudo-types over Q.
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  • Around independence and domination in metric abstract elementary classes: assuming uniqueness of limit models.Andrés Villaveces & Pedro Zambrano - 2014 - Mathematical Logic Quarterly 60 (3):211-227.
    We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular, we study notions that behave well under superstability‐like assumptions. Also, under uniqueness of limit models, we study domination, orthogonality and parallelism of Galois types in MAECs.
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  • Superstable theories with few countable models.Lee Fong Low & Anand Pillay - 1992 - Archive for Mathematical Logic 31 (6):457-465.
    We prove here:Theorem. LetT be a countable complete superstable non ω-stable theory with fewer than continuum many countable models. Then there is a definable groupG with locally modular regular generics, such thatG is not connected-by-finite and any type inG eq orthogonal to the generics has Morley rank.Corollary. LetT be a countable complete superstable theory in which no infinite group is definable. ThenT has either at most countably many, or exactly continuum many countable models, up to isomorphism.
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  • Vaught’s conjecture for superstable theories of finite rank.Steven Buechler - 2008 - Annals of Pure and Applied Logic 155 (3):135-172.
    In [R. Vaught, Denumerable models of complete theories, in: Infinitistic Methods, Pregamon, London, 1961, pp. 303–321] Vaught conjectured that a countable first order theory has countably many or 20 many countable models. Here, the following special case is proved.
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  • Weakly minimal formulas: a global approach.Ludomir Newelski - 1990 - Annals of Pure and Applied Logic 46 (1):65-94.
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  • Non-totally transcendental unidimensional theories.Anand Pillay & Philipp Rothmaler - 1990 - Archive for Mathematical Logic 30 (2):93-111.
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  • Locally finite weakly minimal theories.James Loveys - 1991 - Annals of Pure and Applied Logic 55 (2):153-203.
    Suppose T is a weakly minimal theory and p a strong 1-type having locally finite but nontrivial geometry. That is, for any M [boxvR] T and finite Fp, there is a finite Gp such that acl∩p = gεGacl∩pM; however, we cannot always choose G = F. Then there are formulas θ and E so that θεp and for any M[boxvR]T, E defines an equivalence relation with finite classes on θ/E definably inherits the structure of either a projective or affine space (...)
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  • Semisimple stable and superstable groups.J. T. Baldwin & A. Pillay - 1989 - Annals of Pure and Applied Logic 45 (2):105-127.
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