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Andrei S. Morozov [5]Andrei Morozov [4]
  1.  15
    Effective Categoricity of Equivalence Structures.Wesley Calvert, Douglas Cenzer, Valentina Harizanov & Andrei Morozov - 2006 - Annals of Pure and Applied Logic 141 (1):61-78.
    We investigate effective categoricity of computable equivalence structures . We show that is computably categorical if and only if has only finitely many finite equivalence classes, or has only finitely many infinite classes, bounded character, and at most one finite k such that there are infinitely many classes of size k. We also prove that all computably categorical structures are relatively computably categorical, that is, have computably enumerable Scott families of existential formulas. Since all computable equivalence structures are relatively categorical, (...)
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  2.  9
    Effective Categoricity of Abelian P -Groups.Wesley Calvert, Douglas Cenzer, Valentina S. Harizanov & Andrei Morozov - 2009 - Annals of Pure and Applied Logic 159 (1-2):187-197.
    We investigate effective categoricity of computable Abelian p-groups . We prove that all computably categorical Abelian p-groups are relatively computably categorical, that is, have computably enumerable Scott families of existential formulas. We investigate which computable Abelian p-groups are categorical and relatively categorical.
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  3.  24
    On Σ‐Definability Without Equality Over the Real Numbers.Andrei S. Morozov & Margarita V. Korovina - 2008 - Mathematical Logic Quarterly 54 (5):535-544.
    In [5] it has been shown that for first-order definability over the reals there exists an effective procedure which by a finite formula with equality defining an open set produces a finite formula without equality that defines the same set. In this paper we prove that there exists no such procedure for Σ-definability over the reals. We also show that there exists even no uniform effective transformation of the definitions of Σ-definable sets into new definitions of Σ-definable sets in such (...)
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  4.  9
    Dependence Relations in Computably Rigid Computable Vector Spaces.Rumen D. Dimitrov, Valentina S. Harizanov & Andrei S. Morozov - 2005 - Annals of Pure and Applied Logic 132 (1):97-108.
    We construct a computable vector space with the trivial computable automorphism group, but with the dependence relations as complicated as possible, measured by their Turing degrees. As a corollary, we answer a question asked by A.S. Morozov in [Rigid constructive modules, Algebra and Logic, 28 570–583 ; 379–387 ].
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  5.  20
    Sequences of N-Diagrams.Valentina S. Harizanov, Julia F. Knight & Andrei S. Morozov - 2002 - Journal of Symbolic Logic 67 (3):1227-1247.
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  6.  8
    Preface.Yuri L. Ershov, Klaus Keimel, Ulrich Kohlenbach & Andrei Morozov - 2009 - Annals of Pure and Applied Logic 159 (3):249-250.
  7.  5
    Foreword.Ulrich Berger, Vasco Brattka, Andrei S. Morozov & Dieter Spreen - 2012 - Annals of Pure and Applied Logic 163 (8):973-974.
  8.  2
    Partial Automorphism Semigroups.Jennifer Chubb, Valentina S. Harizanov, Andrei S. Morozov, Sarah Pingrey & Eric Ufferman - 2008 - Annals of Pure and Applied Logic 156 (2):245-258.
    We study the relationship between algebraic structures and their inverse semigroups of partial automorphisms. We consider a variety of classes of natural structures including equivalence structures, orderings, Boolean algebras, and relatively complemented distributive lattices. For certain subsemigroups of these inverse semigroups, isomorphism of the subsemigroups yields isomorphism of the underlying structures. We also prove that for some classes of computable structures, we can reconstruct a computable structure, up to computable isomorphism, from the isomorphism type of its inverse semigroup of computable (...)
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