Algebra and Logic

, Volume 54, Issue 6, pp 428–439 | Cite as

Index Sets of Constructive Models of Finite and Graph Signatures that are Autostable Relative to Strong Constructivizations

  • S. S. GoncharovEmail author
  • M. I. MarchukEmail author

We estimate algorithmic complexity of the class of computable models of finite and graph signatures that have a strong constructivization and are autostable relative to strong constructivizations.


model computable model constructive model autostability index sets 


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  1. 1.
    S. S. Goncharov and Yu. L. Ershov, Constructive Models, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1996).Google Scholar
  2. 2.
    C. J. Ash and J. F. Knight, Computable Structures and the Hyperarithmetical Hierarchy, Stud. Log. Found. Math., 144, Elsevier, Amsterdam (2000).Google Scholar
  3. 3.
    S. S. Goncharov and J. F. Knight, “Computable structure and non-structure theorems,” Algebra and Logic, 41, No. 6, 351–373 (2002).Google Scholar
  4. 4.
    S. S. Goncharov, “Computability and computable models,” in: Int. Math. Ser. (New York), 5, Springer, New York (2007), pp. 99–216.Google Scholar
  5. 5.
    S. S. Goncharov, “Index sets of almost prime constructive models,” Vestnik NGU, Mat., Mekh., Inf., 13, No. 3, 38–52 (2013).Google Scholar
  6. 6.
    E. B. Fokina, “Index sets of decidable models,” Sib. Math. J., 48, No. 5, 939–948 (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    E. N. Pavlovskii, “Estimation of the algorithmic complexity of classes of computable models,” Sib. Math. J., 49, No. 3, 512–523 (2008).MathSciNetCrossRefGoogle Scholar
  8. 8.
    E. N. Pavlovskii, “Index sets of prime models,” Sib. El. Mat. Izv., 5, 200–210 (2008).MathSciNetGoogle Scholar
  9. 9.
    N. A. Bazhenov, “Hyperarithmetical categoricity of Boolean algebras of type B(ω α × η),” Vestnik NGU, Mat., Mekh., Inf., 12, No. 3, 35–45 (2012).Google Scholar
  10. 10.
    N. A. Bazhenov, “Δ2 0-categoricity of Boolean algebras,” Vestnik NGU, Mat., Mekh., Inf., 13, No. 2, 3–14 (2013).Google Scholar
  11. 11.
    S. S. Goncharov and M. I. Marchuk, “Index sets of constructive models of bounded signature that are autostable relative to strong constructivizations,” Algebra and Logic, 54, No. 2, 108–126 (2015).Google Scholar
  12. 12.
    A. T. Nurtazin, “Computable classes and algebraic criteria for autostability,” Ph. D. Thesis, Institute of Mathematics and Mechanics, Alma-Ata (1974).Google Scholar
  13. 13.
    S. S. Goncharov, “The problem of the number of nonautoequivalent constructivizations,” Algebra and Logic, 19, No. 6, 401–414 (1980).Google Scholar
  14. 14.
    A. T. Nurtazin, “Strong and weak constructivizations and computable families,” Algebra and Logic, 13, No. 3, 177–184 (1974).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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