Skip to main content
Log in

Index Sets of Constructive Models that are Autostable Under Strong Constructivizations

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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).

  2. A. T. Nurtazin, “Computable Classes and Algebraic Autostability Criteria” [in Russian], Thesis, Alma-Ata (1974).

  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).

  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).

  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).

  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).

  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).

  8. E. N. Pavlovskii, “Index sets of prime models” [in Russian], Sib. Electr. Mat. Izv. 5, 200–210 (2008).

    MathSciNet  Google Scholar 

  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).

  10. D. Marker, “Non-σ n -axiomatizable almost strongly minimal theories,” J. Symb. Log. 54, No. 3, 921–927 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  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);

  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).

  13. H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).

    MATH  Google Scholar 

  14. Yu. L. Ershov and E. A. Palyutin, Matematical Logic [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  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).

  16. S. S. Goncharov, Countable Boolean Algebras and Decidability, Kluwer Academic/Plenum Publishers, New York (1997).

    MATH  Google Scholar 

  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).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. S. Goncharov.

Additional information

Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 13, No. 4, 2013, pp. 43-67.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goncharov, S.S., Marchuk, M.I. Index Sets of Constructive Models that are Autostable Under Strong Constructivizations. J Math Sci 205, 368–388 (2015). https://doi.org/10.1007/s10958-015-2253-4

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-015-2253-4

Keywords

Navigation