Search results for 'Yegan Pillay' (try it on Scholar)

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  1. Yegan Pillay, Katherine K. Ziff & Christine Suniti Bhat (2008). Vedānta Personality Development: A Model to Enhance the Cultural Competence of Psychotherapists. [REVIEW] International Journal of Hindu Studies 12 (1):65-79.score: 240.0
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  2. Yegan Pillay (2010). Reconceiving Schizophrenia. Philosophical Psychology 23 (5):707-711.score: 240.0
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  3. Anand Pillay (1987). First Order Topological Structures and Theories. Journal of Symbolic Logic 52 (3):763-778.score: 30.0
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  4. Anand Pillay & Thomas Scanlon (2002). Compact Complex Manifolds with the DOP and Other Properties. Journal of Symbolic Logic 67 (2):737-743.score: 30.0
    We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a Kahler manifold to be totally degenerate (that is, to be an indiscernible set, in its canonical language) and point out that there are K3 surfaces which satisfy these conditions.
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  5. Samuel R. Buss, Alexander S. Kechris, Anand Pillay & Richard A. Shore (2001). The Prospects for Mathematical Logic in the Twenty-First Century. Bulletin of Symbolic Logic 7 (2):169-196.score: 30.0
    The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.
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  6. Anand Pillay & Bruno Poizat (1995). Corps Et Chirurgie. Journal of Symbolic Logic 60 (2):528-533.score: 30.0
    Les corps algébriquement clos, réels clos et pseudo-finis n'ont, pour chaque entier n, qu'un nombre fini d'extensions de degré n; nous montrons qu'ils partagent cette propriété avec tous les corps qui, comme eux, satisfont une propriété très rudimentaire de préservation de la dimension, de nature modèle-théorique. Ce résultat est atteint en montrant qu'une certaine action du groupe GLn d'un tel corps n'a qu'un nombre fini d'orbites. /// La korpoj algebre fermataj, reale fermataj kaj pseudofinataj ne havas, pri ciu integro n, (...)
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  7. Anand Pillay (1986). Some Remarks on Definable Equivalence Relations in o-Minimal Structures. Journal of Symbolic Logic 51 (3):709-714.score: 30.0
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  8. Anand Pillay & Gabriel Srour (1984). Closed Sets and Chain Conditions in Stable Theories. Journal of Symbolic Logic 49 (4):1350-1362.score: 30.0
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  9. Anand Pillay & Dominika Polkowska (2006). On PAC and Bounded Substructures of a Stable Structure. Journal of Symbolic Logic 71 (2):460 - 472.score: 30.0
    We introduce and study the notions of a PAC-substructure of a stable structure, and a bounded substructure of an arbitrary substructure, generalizing [10]. We give precise definitions and equivalences, saying what it means for properties such as PAC to be first order, study some examples (such as differentially closed fields) in detail, relate the material to generic automorphisms, and generalize a "descent theorem" for pseudo-algebraically closed fields to the stable context. We also point out that the elementary invariants of pseudo-algebraically (...)
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  10. Ehud Hrushovski, Anand Pillay & Pierre Simon (2012). A Note on Generically Stable Measures and Fsg Groups. Notre Dame Journal of Formal Logic 53 (4):599-605.score: 30.0
    We prove (Proposition 2.1) that if $\mu$ is a generically stable measure in an NIP (no independence property) theory, and $\mu(\phi(x,b))=0$ for all $b$ , then for some $n$ , $\mu^{(n)}(\exists y(\phi(x_{1},y)\wedge \cdots \wedge\phi(x_{n},y)))=0$ . As a consequence we show (Proposition 3.2) that if $G$ is a definable group with fsg (finitely satisfiable generics) in an NIP theory, and $X$ is a definable subset of $G$ , then $X$ is generic if and only if every translate of $X$ does not (...)
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  11. Anand Pillay & Bruno Poizat (1987). PAS d'Imaginaires Dans L'Infini! Journal of Symbolic Logic 52 (2):400-403.score: 30.0
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  12. Anand Pillay & Charles Steinhorn (1987). On Dedekind Complete o-Minimal Structures. Journal of Symbolic Logic 52 (1):156-164.score: 30.0
    For a countable complete o-minimal theory T, we introduce the notion of a sequentially complete model of T. We show that a model M of T is sequentially complete if and only if $\mathscr{M} \prec \mathscr{N}$ for some Dedekind complete model N. We also prove that if T has a Dedekind complete model of power greater than 2 ℵ 0 , then T has Dedekind complete models of arbitrarily large powers. Lastly, we show that a dyadic theory--namely, a theory relative (...)
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  13. Anand Pillay & Wai Yan Pong (2002). On Lascar Rank and Morley Rank of Definable Groups in Differentially Closed Fields. Journal of Symbolic Logic 67 (3):1189-1196.score: 30.0
    Morley rank and Lascar rank are equal on generic types of definable groups in differentially closed fields with finitely many commuting derivations.
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  14. E. Casanovas, D. Lascar, A. Pillay & M. Ziegler (2001). Galois Groups of First Order Theories. Journal of Mathematical Logic 1 (02):305-319.score: 30.0
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  15. Bradd Hart, Byunghan Kim & Anand Pillay (2000). Coordinatisation and Canonical Bases in Simple Theories. Journal of Symbolic Logic 65 (1):293-309.score: 30.0
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  16. Charlotte Kestner & Anand Pillay (2011). Remarks on Unimodularity. Journal of Symbolic Logic 76 (4):1453-1458.score: 30.0
    We clarify and correct some statements and results in the literature concerning unimodularity in the sense of Hrushovski [7], and measurability in the sense of Macpherson and Steinhorn [8], pointing out in particular that the two notions coincide for strongly minimal structures and that another property from [7] is strictly weaker, as well as "completing" Elwes' proof [5] that measurability implies 1-basedness for stable theories.
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  17. Byunghan Kim & Anand Pillay (1998). From Stability to Simplicity. Bulletin of Symbolic Logic 4 (1):17-36.score: 30.0
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  18. D. Marker & A. Pillay (1990). Reducts of (C, +, ⋅) Which Contain +. Journal of Symbolic Logic 55 (3):1243-1251.score: 30.0
    We show that the structure (C,+,·) has no proper non locally modular reducts which contain +. In other words, if $X \subset \mathbf{C}^n$ is constructible and not definable in the module structure (C,+,λ a ) a ∈ C (where λ a denotes multiplication by a) then multiplication is definable in (C,+,X).
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  19. Anand Pillay (1994). Definability of Types, and Pairs of o-Minimal Structures. Journal of Symbolic Logic 59 (4):1400-1409.score: 30.0
    Let T be a complete O-minimal theory in a language L. We first give an elementary proof of the result (due to Marker and Steinhorn) that all types over Dedekind complete models of T are definable. Let L * be L together with a unary predicate P. Let T * be the L * -theory of all pairs (N, M), where M is a Dedekind complete model of T and N is an |M| + -saturated elementary extension of N (and (...)
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  20. Andreas Baudisch & Anand Pillay (2000). A Free Pseudospace. Journal of Symbolic Logic 65 (1):443-460.score: 30.0
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  21. David Marker, Ya'Acov Peterzil & Anand Pillay (1992). Additive Reducts of Real Closed Fields. Journal of Symbolic Logic 57 (1):109-117.score: 30.0
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  22. Anand Pillay & Charles Steinhorn (1985). A Note on Nonmultidimensional Superstable Theories. Journal of Symbolic Logic 50 (4):1020-1024.score: 30.0
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  23. Anand Pillay (2000). A Note on CM-Triviality and the Geometry of Forking. Journal of Symbolic Logic 65 (1):474-480.score: 30.0
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  24. Anand Pillay (2001). A Note on Existentially Closed Difference Fields with Algebraically Closed Fixed Field. Journal of Symbolic Logic 66 (2):719-721.score: 30.0
    We point out that the theory of difference fields with algebraically closed fixed field has no model companion.
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  25. Anand Pillay (1997). Differential Galois Theory II. Annals of Pure and Applied Logic 88 (2-3):181-191.score: 30.0
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  26. Anand Pillay (2003). On Countable Simple Unidimensional Theories. Journal of Symbolic Logic 68 (4):1377-1384.score: 30.0
    We prove that any countable simple unidimensional theory T is supersimple, under the additional assumptions that T eliminates hyperimaginaries and that the $D_\phi-ranks$ are finite and definable.
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  27. A. Pillay & Ž Sokolović (1992). Superstable Differential Fields. Journal of Symbolic Logic 57 (1):97-108.score: 30.0
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  28. Anand Pillay & Martin Ziegler (2004). On a Question of Herzog and Rothmaler. Journal of Symbolic Logic 69 (2):478-481.score: 30.0
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  29. J. T. Baldwin & A. Pillay (1989). Semisimple Stable and Superstable Groups. Annals of Pure and Applied Logic 45 (2):105-127.score: 30.0
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  30. Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev (2003). Lovely Pairs of Models. Annals of Pure and Applied Logic 122 (1-3):235-261.score: 30.0
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  31. S. Barry Cooper, Herman Geuvers, Anand Pillay & Jouko Väänänen (2008). Preface. Annals of Pure and Applied Logic 156 (1):1-2.score: 30.0
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  32. B. Hart, A. Pillay & S. Starchenko (1995). 1-Based Theories — the Main Gap for a -Models. Archive for Mathematical Logic 34 (5):285-300.score: 30.0
    We prove the Main Gap for the class of a -models (sufficiently saturated models) of an arbitrary stable 1-based theory T . We (i) prove a strong structure theorem for a -models, assuming NDOP, and (ii) roughly compute the number of a -models of T in any given cardinality. The analysis uses heavily group existence theorems in 1-based theories.
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  33. Daniel Lascar & Anand Pillay (1999). Forking and Fundamental Order in Simple Theories. Journal of Symbolic Logic 64 (3):1155-1158.score: 30.0
    We give a characterisation of forking in the context of simple theories in terms of the fundamental order.
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  34. Anand Pillay (1997). Remarks on Galois Cohomology and Definability. Journal of Symbolic Logic 62 (2):487-492.score: 30.0
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  35. Anand Pillay (1984). Regular Types in Nonmultidimensional Ω-Stable Theories. Journal of Symbolic Logic 49 (3):880-891.score: 30.0
    We define a hierarchy on the regular types of an ω-stable nonmultidimensional theory, using generalised notions of algebraic and strongly minimal formulae. As an application we show that any resplendent model of an ω-stable finite-dimensional theory is saturated.
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  36. Anand Pillay (1988). Sheaves of Continuous Definable Functions. Journal of Symbolic Logic 53 (4):1165-1169.score: 30.0
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  37. Anand Pillay (1991). Some Remarks on Modular Regular Types. Journal of Symbolic Logic 56 (3):1003-1011.score: 30.0
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  38. Anand Pillay (1994). Some Remarks on Nonmultidimensional Superstable Theories. Journal of Symbolic Logic 59 (1):151-165.score: 30.0
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  39. Anand Pillay (1995). The Geometry of Forking and Groups of Finite Morley Rank. Journal of Symbolic Logic 60 (4):1251-1259.score: 30.0
    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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  40. Anand Pillay & Philipp Rothmaler (1993). Unidimensional Modules: Uniqueness of Maximal Non-Modular Submodels. Annals of Pure and Applied Logic 62 (2):175-181.score: 30.0
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  41. Anand Pillay (1983). $Aleph_0$-Categoricity Over a Predicate. Notre Dame Journal of Formal Logic 24 (4):527-536.score: 30.0
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  42. Anand Pillay & Saharon Shelah (1985). Classification Theory Over a Predicate. I. Notre Dame Journal of Formal Logic 26 (4):361-376.score: 30.0
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  43. Anand Pillay & Evgueni Vassiliev (2005). On Lovely Pairs and the (∃ y ∈ P ) Quantifier. Notre Dame Journal of Formal Logic 46 (4):491-501.score: 30.0
    Given a lovely pair P ≺ M of models of a simple theory T, we study the structure whose universe is P and whose relations are the traces on P of definable (in ℒ with parameters from M) sets in M. We give a necessary and sufficient condition on T (which we call weak lowness) for this structure to have quantifier-elimination. We give an example of a non-weakly-low simple theory.
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  44. Patricia Blanchette, Kit Fine, Heike Mildenberger, André Nies, Anand Pillay, Alexander Razborov, Alexandra Shlapentokh, John R. Steel & Boris Zilber (2009). Notre Dame, Indiana May 20–May 23, 2009. Bulletin of Symbolic Logic 15 (4).score: 30.0
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  45. Ambar Chowdhury & Anand Pillay (1994). On the Number of Models of Uncountable Theories. Journal of Symbolic Logic 59 (4):1285-1300.score: 30.0
    In this paper we establish the following theorems. THEOREM A. Let T be a complete first-order theory which is uncountable. Then: (i) I(|T|, T) ≥ ℵ 0 . (ii) If T is not unidimensional, then for any λ ≥ |T|, I (λ, T) ≥ ℵ 0 . THEOREM B. Let T be superstable, not totally transcendental and nonmultidimensional. Let θ(x) be a formula of least R ∞ rank which does not have Morley rank, and let p be any stationary completion (...)
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  46. Krzysztof Krupiński, Anand Pillay & Sławomir Solecki (2013). Borel Equivalence Relations and Lascar Strong Types. Journal of Mathematical Logic 13 (2):1350008.score: 30.0
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  47. Lee Fong Low & Anand Pillay (1992). Superstable Theories with Few Countable Models. Archive for Mathematical Logic 31 (6):457-465.score: 30.0
    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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  48. Anand Pillay (1983). A Note on Finitely Generated Models. Journal of Symbolic Logic 48 (1):163-166.score: 30.0
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  49. A. Pillay (1989). A Note on Subgroups of the Automorphism Group of a Saturated Model, and Regular Types. Journal of Symbolic Logic 54 (3):858-864.score: 30.0
    Let $M$ be a saturated model of a superstable theory and let $G = \operatorname{Aut}(M)$. We study subgroups $H$ of $G$ which contain $G_{(A)}, A$ the algebraic closure of a finite set, generalizing results of Lascar [L] as well as giving an alternative characterization of the simple superstable theories of [P]. We also make some observations about good, locally modular regular types $p$ in the context of $p$-simple types.
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  50. Anand Pillay & Wai Yan Pong (2009). Corrigendum To: "On Lascar Rank and Morley Rank of Definable Groups in Differentially Closed Fields". Journal of Symbolic Logic 74 (4):1436 - 1437.score: 30.0
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