Skip to main content
SpringerLink
Log in

Strong noncuppability in low computably enumerable degrees

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We prove the existence of noncomputable low computably enumerable degrees b < a such that b is strongly noncuppable to a in the class R.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Reference

  1. R. I. Soare, Recursively Enumerable Sets and Degrees (Berlin, Springer-Verlag, 1987).

    Google Scholar 

  2. D. P. Miller, “High Recursively Enumerable Degrees and the Anti-Cupping Property,” Lect. Notes Math. 859, 230–245 (1981).

    Article  Google Scholar 

  3. S. B. Cooper, “The Strong Anticupping Property for Recursively Enumerable Degrees,” J. Symbolic Logic 54(2), 527–539 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  4. T. A. Slaman and J. R. Steel, “Complementation in the Turing Degrees,” J. Symbolic Logic 54(1), 160–176 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  5. M. M. Arslanov, “The Stucture of Degrees Below 0′,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 7, 27–33 (1988) [Soviet Mathematics (Iz. VUZ) 32 (7), 25-31 (1988)].

    MathSciNet  Google Scholar 

  6. S. B. Cooper, S. Lempp, and P. Watson, “Weak Density and Cupping in the d-c. e. Degrees,” IsraelJ. of Math. 67, 137–152 (1989).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan State University, 18 Kremlevskaya str., Kazan, 420008, Russia

    M. M. Yamaleev

Authors
  1. M. M. Yamaleev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Yamaleev.

Additional information

Original Russian Text © M.M. Yamaleev, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 4, pp. 83–95.

About this article

Cite this article

Yamaleev, M.M. Strong noncuppability in low computably enumerable degrees. Russ Math. 54, 72–81 (2010). https://doi.org/10.3103/S1066369X10040092

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X10040092

Key words and phrases

Search

Navigation