12 found
  1.  45
    Vapnik–Chervonenkis Density in Some Theories without the Independence Property, II.Matthias Aschenbrenner, Alf Dolich, Deirdre Haskell, Dugald Macpherson & Sergei Starchenko - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):311-363.
    We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.
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  2.  33
    Definable homomorphisms of abelian groups in o-minimal structures.Ya'acov Peterzil & Sergei Starchenko - 1999 - Annals of Pure and Applied Logic 101 (1):1-27.
    We investigate the group of definable homomorphisms between two definable abelian groups A and B, in an o-minimal structure . We prove the existence of a “large”, definable subgroup of . If contains an infinite definable set of homomorphisms then some definable subgroup of B admits a definable multiplication, making it into a field. As we show, all of this can be carried out not only in the underlying structure but also in any structure definable in.
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  3.  29
    Groups Definable in Ordered Vector Spaces over Ordered Division Rings.Pantelis E. Eleftheriou & Sergei Starchenko - 2007 - Journal of Symbolic Logic 72 (4):1108 - 1140.
    Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture (...)
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  4.  26
    Forking in VC-minimal theories.Sarah Cotter & Sergei Starchenko - 2012 - Journal of Symbolic Logic 77 (4):1257-1271.
    We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M, generalizing a result of Dolich on o-minimal theories in [4].
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  5.  23
    On forking and definability of types in some dp-minimal theories.Pierre Simon & Sergei Starchenko - 2014 - Journal of Symbolic Logic 79 (4):1020-1024.
    We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst nonforking types.
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  6.  46
    Geometry, calculus and Zil'ber's conjecture.Ya'acov Peterzil & Sergei Starchenko - 1996 - Bulletin of Symbolic Logic 2 (1):72-83.
    §1. Introduction. By and large, definitions of a differentiable structure on a set involve two ingredients, topology and algebra. However, in some cases, partial information on one or both of these is sufficient. A very simple example is that of the field ℝ where algebra alone determines the ordering and hence the topology of the field:In the case of the field ℂ, the algebraic structure is insufficient to determine the Euclidean topology; another topology, Zariski, is associated with the ield but (...)
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  7.  28
    Expansions of algebraically closed fields II: Functions of several variables.Ya'acov Peterzil & Sergei Starchenko - 2003 - Journal of Mathematical Logic 3 (01):1-35.
    Let ℛ be an o-minimal expansion of a real closed field R. We continue here the investigation we began in [11] of differentiability with respect to the algebraically closed field [Formula: see text]. We develop the basic theory of such K-differentiability for definable functions of several variables, proving theorems on removable singularities as well as analogues of the Weierstrass preparation and division theorems for definable functions. We consider also definably meromorphic functions and prove that every definable function which is meromorphic (...)
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  8.  22
    Introduction.Zoé Chatzidakis, David Marker, Amador Martin-Pizarro, Rahim Moosa & Sergei Starchenko - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):277-277.
    Zoé Chatzidakis , David Marker , Amador Martin-Pizarro , Rahim Moosa , Sergei Starchenko Source: Notre Dame J. Formal Logic, Volume 54, Number 3-4, 277--277.
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  9.  29
    San Antonio Convention Center San Antonio, Texas January 14–15, 2006.Douglas Cenzer, C. Ward Henson, Michael C. Laskowski, Alain Louveau, Russell Miller, Itay Neeman, Sergei Starchenko & Valentina Harizanov - 2006 - Bulletin of Symbolic Logic 12 (4).
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  10.  12
    Model-theoretic Elekes–Szabó in the strongly minimal case.Artem Chernikov & Sergei Starchenko - 2020 - Journal of Mathematical Logic 21 (2):2150004.
    We prove a generalization of the Elekes–Szabó theorem [G. Elekes and E. Szabó, How to find groups?, Combinatorica 32 537–571 ] for relations defina...
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  11.  35
    Madison, WI, USA March 31–April 3, 2012.Alan Dow, Isaac Goldbring, Warren Goldfarb, Joseph Miller, Toniann Pitassi, Antonio Montalbán, Grigor Sargsyan, Sergei Starchenko & Moshe Vardi - 2013 - Bulletin of Symbolic Logic 19 (2).
  12.  19
    Addendum to "a structure theorem for strongly Abelian varieties".Bradd Hart & Sergei Starchenko - 1993 - Journal of Symbolic Logic 58 (4):1419-1425.