Algebra and Logic

, Volume 54, Issue 2, pp 108–126 | Cite as

Index Sets of Constructive Models of Bounded Signature that are Autostable Relative to Strong Constructivizations

Article

We evaluate algorithmic complexity of the class of computable models of bounded signature that have a strong constructivization and are autostable relative to strong constructivizations.

Keywords

model computable model constructive model autostability index sets 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. S. Goncharov and J. F. Knight, “Computable structure and non-structure theorems,” Algebra and Logic, 41, No. 6, 351–373 (2002).MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. T. Nurtazin, “Computable classes and algebraic criteria for autostability,” Ph. D. Thesis, Institute of Mathematics and Mechanics, Alma-Ata (1974).Google Scholar
  3. 3.
    S. S. Goncharov and Yu. L. Ershov, Constructive Models, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1996).Google Scholar
  4. 4.
    S. S. Goncharov, “The problem of the number of non-autoequivalent constructivizations,” Dokl. Akad. Nauk SSSR, 251, No. 2, 271–274 (1980).MathSciNetGoogle Scholar
  5. 5.
    S. S. Goncharov, “Computability and computable models,” in: Int. Math. Ser. (New York), 5, Springer, New York (2007), pp. 99–216.Google Scholar
  6. 6.
    E. B. Fokina, “Index sets of decidable models,” Sib. Math. J., 48, No. 5, 939–948 (2007).MathSciNetCrossRefGoogle 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 model,” Sib. El. Mat. Izv., 5, 200–210 (2008).MathSciNetGoogle Scholar
  9. 9.
    Yu. L. Ershov and E. A. Palyutin, Mathematical Logic [in Russian], 6th ed., Fizmatlit, Moscow (2011).Google Scholar
  10. 10.
    H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).MATHGoogle Scholar
  11. 11.
    S. S. Goncharov and A. T. Nurtazin, “Constructive models of complete solvable theories,” Algebra and Logic, 12, No. 2, 67–77 (1973).CrossRefGoogle Scholar
  12. 12.
    A. T. Nurtazin, “Strong and weak constructivizations and computable families,” Algebra and Logic, 13, No. 3, 177–184 (1974).CrossRefGoogle Scholar
  13. 13.
    S. S. Goncharov, “Index sets of almost prime constructive models,” Vestnik NGU, Mat., Mekh., Inf., 13, No. 3, 38–52 (2013).Google Scholar
  14. 14.
    S. S. Goncharov and B. Khoussainov, “Complexity of categorical theories with computable models,” Algebra and Logic, 43, No. 6, 365–373 (2004).MathSciNetCrossRefGoogle Scholar
  15. 15.
    S. S. Goncharov, Countable Boolean Algebras and Decidability, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1996).Google Scholar
  16. 16.
    M. G. Peretyatkin, “Strongly constructive models and enumerations for the Boolean algebra of recursive sets,” Algebra and Logic, 10, No. 5, 332–345 (1971).MathSciNetCrossRefGoogle Scholar
  17. 17.
    D. Marker, “Non Σn axiomatizable almost strongly minimal theories,” J. Symb. Log., 54, No. 3, 921–927 (1989).MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    S. S. Goncharov and M. I. Marchuk, “Index sets of constructive models that are autostable under strong constructivizations,” Vestnik NGU, Mat., Mekh., Inf., 13, No. 4, 43–67 (2013).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

Personalised recommendations