Университеттің 85 жылдығына арналған Қазіргі заманғы математика
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- Keywords: externally definable, neighborhood of tuple of the set in the type, non orthogonality of two types. List of literature
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внешне определимый, окрестность кортежа множества по типу, неортогональность двух типов. Expansion of a model by unary externally definable set and neighborhood of element in type Annotation The reports discusses the various approaches to the concept of external definability developed in o-minimal theories. In conclusion, su ffi cient conditions are formulated so that the theory has the property of external definability. A brief explanation of the stated theorem is given. Keywords: externally definable, neighborhood of tuple of the set in the type, non orthogonality of two types. List of literature: [1] D. Macpherson, D. Marker, Ch. Steinhorn, Weakly o-minimal structures and real closed fields , Translations of the American Mathematical Society, 352 (2000),5435–5483. [2] B.S. Baizhanov, Extensions of o-minimal structures by convex unary predicates , In the book: "Research in the theory of algebraic systems" (editor T.A. Nur- magambetov),KaragandaStateUniversity,1995,6–24.(inRussian) [3] A.Pillay, C.Steinhorn, Definable sets in ordered structures , Bulletin AMS,11 (1984),159–162. [4] A. Pillay, C. Steinhorn, Definable sets in ordered structures I , Transactions of American Mathematical Society, 295 (1986),565–592. [5] D. Marker, Omitting types in o-minimal theories , The Journal of Symbolic Logic, 51 (1986),63–74. [6] L. Mayer, Vaught’s conjecture for o-minimal theories , The Journal of Symbolic Logic, 53 (1988),146–159. [7] A.Pillay, Ch.Steinhorn, Definable sets in ordered structures III , Transactions of the American Mathematical Society, 300 (1988), 469–476. [8] D.Marker, Ch. Steinhorn, Definable types in o-minimal theories , The Journal of Symbolic Logic, 59 (1994), 185–198. [9] B.S.Baizhanov, Expansion of a model of a weakly o-minimal theory by a family of unary predicates , The Journal of Symbolic Logic, 66 (2001), 1382–1414. [10] S. Shelah, Dependent first order theories. Continued , Israel Journal of Mathematics 173 : 1. (2009) https://doi.org/10.1007/s11856-009-0082-1 [11] V. Verbovskiy, Dependent theories. The Shelah’s theorem , Proceeding of International conference "Contemporary problems of mathematics, informatics and control", dedicated to 60th anniversary of M.B. Aidarkhanov, October 2-3, 2008, Almaty, 439–441 A.Pillay, On externally definable sets and a theorem of Shelah , Algebra, logic, set theory, Stud. Log.(Lond.), (2007) pdfs.semanticscholar.org |