Skip to main content

Co-total Enumeration Degrees

  • Conference paper
Logical Approaches to Computational Barriers (CiE 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3988))

Included in the following conference series:

Abstract

This paper is dedicated to the study of the enumeration degrees which contain sets the complements of which are the graphs of some total functions. Such e-degrees are called co-total. That every total e-degree a0 e contains such total function f that \({\rm deg}_e(\overline{{\rm graph}(f)})\) is a quasi-minimal e-degree has been proved. Some known results of McEvoy and Gutteridge with the aid of co-total e-degrees become stronger as well.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arslanov, M.M., Cooper, S.B., Kalimullin, I.S.: The properties of the splitting of total e-degrees. Algebra i Logica 43, 1–25 (2003)

    Article  MATH  Google Scholar 

  2. Case, J.: Enumeration reducibility and partial degreees. Annals Math. Logic 2, 419–439 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fridberg, R., Rogers, H.: Reducibility and completness for sets of integers. Z. math. Logic Grundl. Math. 5, 117–125 (1959)

    Article  Google Scholar 

  4. Gutteridge, L.: Some results on e-reducibility. Ph.D.Diss (1971)

    Google Scholar 

  5. McEvoy, K.: Jumps of quasi-minimal enumeration degrees. J. Symb. Logic 50, 839–848 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  6. Medvedev Yu, T.: Degrees of difficulty of the mass problem. Dokl. Acad. Nauk SSSR 104, 501–504 (1955)

    MathSciNet  Google Scholar 

  7. Pankratov, A.: The research of some properties of co-total e-degrees. In: Intern. conf. “Logic and applications”, Proceedings, Novosibirsk, vol. 79 (2000)

    Google Scholar 

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

    MATH  Google Scholar 

  9. Sasso, L.P.: A survey of partial degrees. J. Symb. Logic 40, 130–140 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  10. Soar Robert, I.: Recursively Enumerable Sets and Degrees. Springer, Heidelberg (1987)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Solon, B. (2006). Co-total Enumeration Degrees. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_55

Download citation

  • DOI: https://doi.org/10.1007/11780342_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35466-6

  • Online ISBN: 978-3-540-35468-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics