Journal of Mathematical Sciences

, Volume 205, Issue 3, pp 368–388 | Cite as

Index Sets of Constructive Models that are Autostable Under Strong Constructivizations

  • S. S. GoncharovEmail author
  • M. I. Marchuk

We obtain estimates for the algorithmic complexity of index sets for the class of decidable autostable models and the class of computable models that possess strong constructivizations and are autostable under strong constructivizations.


Computable Function Constructive Model Predicate Symbol Constant Symbol Computable Numbering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. S. Goncharov and J. F. Knight, “Computable structure and non-structure theorems” [in Russian], Algebra Logika 41, No. 6, 639–681 (2002); English transl.: Algebra Logic 41, No. 6, 351–373 (2002).Google Scholar
  2. 2.
    A. T. Nurtazin, “Computable Classes and Algebraic Autostability Criteria” [in Russian], Thesis, Alma-Ata (1974).Google Scholar
  3. 3.
    S. S. Goncharov and Yu. L. Ershov, Constructive Models [in Russian], Nauchnaya kniga (IDMI), Novosibirsk (1999); English transl.: Kluwer Academic/Plenum Press, New York (2002).Google Scholar
  4. 4.
    S. S. Goncharov, “Problem of the number of non-self-equivalent constructivizations” [in Russian], Algebra Logika 19, No. 6. 621–639 (1980); English transl.: S. S. Goncharov Algebra Logic 19, No. 6. 401–414 (1980).Google Scholar
  5. 5.
    S. S. Goncharov, “Computability and computable models, mathematical problems from applied logic. II,” In: Logics for the XXIst Century, pp. 99–216, Springer, New York (2006).Google Scholar
  6. 6.
    E. B. Fokina, “Index sets of decidable models” [in Russian], Sib. Mat. Zh. 48, No. 5, 1167–1179 (2007); English transl.: Sib. Math. J. 48, No. 5, 939–948 (2007).Google Scholar
  7. 7.
    E. N. Pavlovskii, “Estimation of the algorithmic complexity of classes of computable models” [in Russian], Sib. Mat. Zh. 49, No. 3, 635–649 (2008); English transl.: Sib. Math. J. 49, No. 3, 512–523 (2008).Google Scholar
  8. 8.
    E. N. Pavlovskii, “Index sets of prime models” [in Russian], Sib. Electr. Mat. Izv. 5, 200–210 (2008).MathSciNetGoogle Scholar
  9. 9.
    S. S. Goncharov and B. Khoussainov, “Complexity of categorical theories with computable models” [in Russian], Algebra Logika 43, No. 6, 650-665 (2004); English transl.: Algebra Logic 43, No. 6, 365-373 (2004).Google Scholar
  10. 10.
    D. Marker, “Non-σ n-axiomatizable almost strongly minimal theories,” J. Symb. Log. 54, No. 3, 921–927 (1989).CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    A. T. Nurtazin, “Strong and weak constructivizations and computable families” [in Russian], Algebra Logika 13, No. 3, 311–323 (1974); English transl.: Algebra Logic 13, No. 3, 177–184 (1974);Google Scholar
  12. 12.
    S. S. Goncharov, “Index sets of almost prime constructive models” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13, No. 3, 38–52 (2013); English transl.: J. Math. Sci., New York 205, No. 3, 355–367 (2015).Google Scholar
  13. 13.
    H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).zbMATHGoogle Scholar
  14. 14.
    Yu. L. Ershov and E. A. Palyutin, Matematical Logic [in Russian], Nauka, Moscow (1987).Google Scholar
  15. 15.
    S. S. Goncharov and A. T. Nurtazin, “Constructive models of complete solvable theories” [in Russian], Algebra Logika 12, No. 2, 125–142 (1973); English transl.: Algebra Logic 12, 67–77 (1974).Google Scholar
  16. 16.
    S. S. Goncharov, Countable Boolean Algebras and Decidability, Kluwer Academic/Plenum Publishers, New York (1997).zbMATHGoogle Scholar
  17. 17.
    M. G. Peretyat’kin, “Strongly constructive models and numerations of the Boolean algebra of recursive sets” [in Russian], Algebra Logika 10, 535-537 (1971); English transl.: Algebra Logic 10, 332-345 (1973).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations