Skip to main content
Log in

Structural Theory of Degrees of Unsolvability: Advances and Open Problems

  • COMMUNICATIONS
  • Published:
Algebra and Logic Aims and scope

Presented by the Program Committee of the Conference “Mal’tsev Readings”

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. Lempp, M. Lerman, and D. Solomon, “Embedding finite lattices into the computably enumerable degrees—a status survey,” in Lect. Notes Log., 27, Assoc. Symb. Log., Urbana, IL (2006), pp. 206–229.

  2. T. A. Slaman and R. I. Soare, “Extension of embeddings in the computably enumerable degrees,” Ann. Math. (2), 154, No. 1, 1–43 (2001).

  3. K. Ambos-Spies, C. G. Jun. Jockusch, R. A. Shore, and R. I. Soare, “An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees,” Trans. Am. Math. Soc., 281, 109–128 (1984).

  4. M. Lerman, Degrees of Unsolvability. Local and Global Theory, Perspect. Math. Log., Springer-Verlag, Berlin (1983).

  5. M. M. Arslanov, I. Sh. Kalimullin, and S. Lempp, “On Downey’s conjecture,” J. Symb. Log., 75, No. 2, 401–441 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  6. K. Ambos-Spies and M. Lerman, “Lattice embeddings into the recursively enumerable degrees,” J. Symb. Log., 51, 257–272 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  7. K. Ambos-Spies and M. Lerman, “Lattice embeddings into the recursively enumerable degrees. II,” J. Symb. Log., 54, No. 3, 735–760 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Downey, “D-r.e. degrees and the nondiamond theorem,” Bull. London Math. Soc., 21, No. 1, 43–50 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Li and X. Yi, “Cupping the recursively enumerable degrees by d.r.e. degrees,” Proc. London Math. Soc., III. Ser., 79, No. 1, 1–21 (1999).

  10. G. Barmpalias, M. Cai, S. Lempp, and T. A. Slaman, “On the existence of a strong minimal pair,” J. Math. Log., 15, No. 1; DOI: 10.1142/S0219061315500026.

  11. M. M. Arslanov, “On the structure of degrees below 0′,” Izv. Vyssh. Uch. Zav., Ser. Mat., No. 7, 27–34 (1988).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. M. Arslanov.

Additional information

(M. M. Arslanov) Supported by RFBR (project Nos. 15-01-08252 and 15-41-02507).

Translated from Algebra i Logika, Vol. 54, No. 4, pp. 529–535, July-August, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arslanov, M.M. Structural Theory of Degrees of Unsolvability: Advances and Open Problems. Algebra Logic 54, 342–346 (2015). https://doi.org/10.1007/s10469-015-9354-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-015-9354-5

Keywords

Navigation