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Sergey Goncharov [5]Sergey S. Goncharov [3]
  1.  24
    Enumerations in Computable Structure Theory.Sergey Goncharov, Valentina Harizanov, Julia Knight, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Annals of Pure and Applied Logic 136 (3):219-246.
    We exploit properties of certain directed graphs, obtained from the families of sets with special effective enumeration properties, to generalize several results in computable model theory to higher levels of the hyperarithmetical hierarchy. Families of sets with such enumeration features were previously built by Selivanov, Goncharov, and Wehner. For a computable successor ordinal α, we transform a countable directed graph into a structure such that has a isomorphic copy if and only if has a computable isomorphic copy.A computable structure is (...)
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  2.  34
    Computably Categorical Structures and Expansions by Constants.Peter Cholak, Sergey Goncharov, Bakhadyr Khoussainov & Richard A. Shore - 1999 - Journal of Symbolic Logic 64 (1):13-37.
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  3.  23
    Π 1 1 Relations and Paths Through.Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Richard A. Shore - 2004 - Journal of Symbolic Logic 69 (2):585-611.
  4.  50
    Intrinsic Bounds on Complexity and Definability at Limit Levels.John Chisholm, Ekaterina B. Fokina, Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Sara Quinn - 2009 - Journal of Symbolic Logic 74 (3):1047-1060.
    We show that for every computable limit ordinal α, there is a computable structure A that is $\Delta _\alpha ^0 $ categorical, but not relatively $\Delta _\alpha ^0 $ categorical (equivalently. it does not have a formally $\Sigma _\alpha ^0 $ Scott family). We also show that for every computable limit ordinal a, there is a computable structure A with an additional relation R that is intrinsically $\Sigma _\alpha ^0 $ on A. but not relatively intrinsically $\Sigma _\alpha ^0 $ (...)
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  5.  13
    Some Effectively Infinite Classes of Enumerations.Sergey Goncharov, Alexander Yakhnis & Vladimir Yakhnis - 1993 - Annals of Pure and Applied Logic 60 (3):207-235.
    This research partially answers the question raised by Goncharov about the size of the class of positive elements of a Roger's semilattice. We introduce a notion of effective infinity of classes of computable enumerations. Then, using finite injury priority method, we prove five theorems which give sufficient conditions to be effectively infinite for classes of all enumerations without repetitions, positive undecidable enumerations, negative undecidable enumerations and all computable enumerations of a family of r.e. sets. These theorems permit to strengthen the (...)
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  6.  5
    Π₁¹ Relations and Paths Through ᵊ.Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Richard A. Shore - 2004 - Journal of Symbolic Logic 69 (2):585 - 611.