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  1. Hyperimaginaries and Automorphism Groups.D. Lascar & A. Pillay - 2001 - Journal of Symbolic Logic 66 (1):127-143.
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  • Coordinatisation and canonical bases in simple theories.Bradd Hart, Byunghan Kim & Anand Pillay - 2000 - Journal of Symbolic Logic 65 (1):293-309.
    In this paper we discuss several generalization of theorems from stability theory to simple theories. Cherlin and Hrushovski, in [2] develop a substitute for canonical bases in finite rank, ω-categorical supersimple theories. Motivated by methods there, we prove the existence of canonical bases (in a suitable sense) for types in any simple theory. This is done in Section 2. In general these canonical bases will (as far as we know) exist only as “hyperimaginaries”, namely objects of the forma/Ewhereais a possibly (...)
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  • The geometry of forking and groups of finite Morley rank.Anand Pillay - 1995 - Journal of Symbolic Logic 60 (4):1251-1259.
    The notion of CM-triviality was introduced by Hrushovski, who showed that his new strongly minimal sets have this property. Recently Baudisch has shown that his new ω 1 -categorical group has this property. Here we show that any group of finite Morley rank definable in a CM-trivial theory is nilpotent-by-finite, or equivalently no simple group of finite Morley rank can be definable in a CM-trivial theory.
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  • (1 other version)[Omnibus Review].Anand Pillay - 1984 - Journal of Symbolic Logic 49 (1):317-321.
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  • (1 other version)Simplicity, and stability in there.Byunghan Kim - 2001 - Journal of Symbolic Logic 66 (2):822-836.
    Firstly, in this paper, we prove that the equivalence of simplicity and the symmetry of forking. Secondly, we attempt to recover definability part of stability theory to simplicity theory. In particular, using elimination of hyperimaginaries we prove that for any supersimple T, canonical base of an amalgamation class P is the union of names of ψ-definitions of P, ψ ranging over stationary L-formulas in P. Also, we prove that the same is true with stable formulas for an 1-based theory having (...)
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  • PAS d'imaginaires dans l'infini!Anand Pillay & Bruno Poizat - 1987 - Journal of Symbolic Logic 52 (2):400-403.
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  • Ample thoughts.Daniel Palacín & Frank O. Wagner - 2013 - Journal of Symbolic Logic 78 (2):489-510.
    Non-$n$-ampleness as defined by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of $\Sigma$-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groups.
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  • (1 other version)A note on Lascar strong types in simple theories.Byunghan Kim - 1998 - Journal of Symbolic Logic 63 (3):926-936.
    Let T be a countable, small simple theory. In this paper, we prove that for such T, the notion of Lascar strong type coincides with the notion of strong type, over an arbitrary set.
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  • (1 other version)A note on Lascar strong types in simple theories.Byunghan Kim - 1998 - Journal of Symbolic Logic 63 (3):926-936.
    LetTbe a countable, small simple theory. In this paper, we prove that for suchT, the notion of Lascar strong type coincides with the notion of strong type, over an arbitrary set.
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  • On the automorphism groups of finite covers.David M. Evans & Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):83-112.
    We are concerned with identifying by how much a finite cover of an 0-categorical structure differs from a sequence of free covers. The main results show that this is measured by automorphism groups which are nilpotent-by-abelian. In the language of covers, these results say that every finite cover can be decomposed naturally into linked, superlinked and free covers. The superlinked covers arise from covers over a different base, and to describe this properly we introduce the notion of a quasi-cover.These results (...)
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