Skip to main content
Log in

Complexity of Isomorphism Problem for Computable Projective Planes

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

We study computable presentations for projective planes. We show that the isomorphism problem is Σ 11 complete for Pappian projective planes, Desarguesian projective planes, and arbitrary projective planes. Bibliography: 11 titles.

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. A. S. Morozov, “Functional trees and automorphisms of models”, [in Russian], Algebra Logika 32, No. 1, 54–72 (1993); English transl.: Algebra Logic 32, No. 1, 28–38 (1993).

    Article  Google Scholar 

  2. A. Nies, “Undecidable fragments of elementary theories,” Algebra Univers. 35, No. 1, 8–33 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  3. 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).

    Article  MathSciNet  Google Scholar 

  4. D. Hirschfeldt, B. Khoussainov, B. Shore, and A. M. Slinko, “Degree spectra and computable dimensions in algebraic structures,” Ann. Pure Appl. Logic 115, No. 1–3, 71–113 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  5. W. Calvert, “The isomorphism problem for classes of computable fields,” Arch. Math. Logic 43, No. 3, 327–336 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  6. W. Calvert, “The isomorphism problem for computable Abelian p-groups of bounded length,” J. Symb. Logic 70, No. 1, 331–345 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  7. A. I. Shirshov and A. A. Nikitin, “On the theory of projective planes,” [in Russian], Algebra Logika 20, No. 3, 330–356 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. I. Shirshov and A. A. Nikitin, Algebraic Theory of Projective Planes, Novosibirsk (1987).

  9. S. S. Goncharov and Yu. L. Ershov, Constructive Models [in Russian], Nauchnaya Kniga (IDMI), Novosibirsk (1999); English transl.: Consultants Bureau, New York (2000).

    Google Scholar 

  10. D. R. Hughes and F. C. Piper, Projective Planes, Springer, New York etc. (1973).

    MATH  Google Scholar 

  11. E. V. Fokina, S. D. Friedman, V. Harizanov, J. F. Knight, C. McCoy, and A. Montalban, “Isomorphism relations on computable structures,” J. Symb. Logic 77, No. 1, 122–132 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. T. Kogabaev.

Additional information

Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 13, No. 1, 2013, pp. 68–75.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kogabaev, N.T. Complexity of Isomorphism Problem for Computable Projective Planes. J Math Sci 203, 509–515 (2014). https://doi.org/10.1007/s10958-014-2154-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-014-2154-y

Keywords

Navigation