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Alexei Kolesnikov [11]Alexei S. Kolesnikov [2]
  1.  12
    Canonical Forking in AECs.Will Boney, Rami Grossberg, Alexei Kolesnikov & Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (7):590-613.
  2.  20
    Type-Amalgamation Properties and Polygroupoids in Stable Theories.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2015 - Journal of Mathematical Logic 15 (1):1550004.
    We show that in a stable first-order theory, the failure of higher dimensional type amalgamation can always be witnessed by algebraic structures that we call n-ary polygroupoids. This generalizes a result of Hrushovski in [16] that failures of 4-amalgamation are witnessed by definable groupoids. The n-ary polygroupoids are definable in a mild expansion of the language.
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  3.  10
    Homology Groups of Types in Model Theory and the Computation of H 2.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2013 - Journal of Symbolic Logic 78 (4):1086-1114.
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  4.  10
    The Amalgamation Spectrum.John T. Baldwin, Alexei Kolesnikov & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (3):914-928.
    We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A For every natural number k, there is a class $K_k $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{k - 1} $ , but $K_k $ has the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_{k - 3} $ and has models of cardinality $\mathfrak{N}_{k (...)
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  5.  8
    The Hanf Number for Amalgamation of Coloring Classes.Alexei Kolesnikov & Chris Lambie-Hanson - 2016 - Journal of Symbolic Logic 81 (2):570-583.
  6.  9
    Generalized Amalgamation and N -Simplicity.Byunghan Kim, Alexei S. Kolesnikov & Akito Tsuboi - 2008 - Annals of Pure and Applied Logic 155 (2):97-114.
    We study generalized amalgamation properties in simple theories. We formulate a notion of generalized amalgamation in such a way so that the properties are preserved when we pass from T to Teq or Theq; we provide several equivalent ways of formulating the notion of generalized amalgamation.We define two distinct hierarchies of simple theories characterized by their amalgamation properties; examples are given to show the difference between the hierarchies.
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  7.  12
    Homology Groups of Types in Model Theory and the Computation of $H_2$.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2013 - Journal of Symbolic Logic 78 (4):1086-1114.
  8.  14
    N-Simple Theories.Alexei S. Kolesnikov - 2005 - Annals of Pure and Applied Logic 131 (1-3):227-261.
    The main topic of this paper is the investigation of generalized amalgamation properties for simple theories. That is, we are trying to answer the question of when a simple theory has the property of n-dimensional amalgamation, where two-dimensional amalgamation is the Independence Theorem for simple theories. We develop the notions of strong n-simplicity and n-simplicity for 1≤n≤ω, where both “1-simple” and “strongly 1-simple” are the same as “simple”. For strong n-simplicity, we present examples of simple unstable theories in each subclass (...)
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  9.  29
    Groupoids, Covers, and 3-Uniqueness in Stable Theories.John Goodrick & Alexei Kolesnikov - 2010 - Journal of Symbolic Logic 75 (3):905-929.
    Building on Hrushovski's work in [5], we study definable groupoids in stable theories and their relationship with 3-uniqueness and finite internal covers. We introduce the notion of retractability of a definable groupoid (which is slightly stronger than Hrushovski's notion of eliminability), give some criteria for when groupoids are retractable, and show how retractability relates to both 3-uniqueness and the splitness of finite internal covers. One application we give is a new direct method of constructing non-eliminable groupoids from witnesses to the (...)
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  10.  7
    Homology Groups of Types in Stable Theories and the Hurewicz Correspondence.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2017 - Annals of Pure and Applied Logic 168 (9):1710-1728.
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  11.  25
    The Equality S1 = D = R.Rami Grossberg, Alexei Kolesnikov, Ivan Tomašić & Monica Van Dieren - 2003 - Mathematical Logic Quarterly 49 (2):115-128.
    The new result of this paper is that for θ-stable we have S1[θ] = D[θ, L, ∞]. S1 is Hrushovski's rank. This is an improvement of a result of Kim and Pillay, who for simple theories under the assumption that either of the ranks be finite obtained the same identity. Only the first equality is new, the second equality is a result of Shelah from the seventies. We derive it by studying localizations of several rank functions, we get the followingMain (...)
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  12.  22
    Morley Rank in Homogeneous Models.Alexei Kolesnikov & G. V. N. G. Krishnamurthi - 2006 - Notre Dame Journal of Formal Logic 47 (3):319-329.
    We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.
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  13.  2
    The Relativized Lascar Groups, Type-Amalgamation, and Algebraicity.Jan Dobrowolski, Byunghan Kim, Alexei Kolesnikov & Junguk Lee - 2021 - Journal of Symbolic Logic 86 (2):531-557.
    In this paper we study the relativized Lascar Galois group of a strong type. The group is a quasi-compact connected topological group, and if in addition the underlying theory T is G-compact, then the group is compact. We apply compact group theory to obtain model theoretic results in this note. -/- For example, we use the divisibility of the Lascar group of a strong type to show that, in a simple theory, such types have a certain model theoretic property that (...)
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