Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T10:35:53.765Z Has data issue: false hasContentIssue false
  • English
  • Français

The distribution of properly Σ20 e-degrees

Published online by Cambridge University Press:  12 March 2014

Stanislaw Bereznyuk ,
Richard Coles  and
Andrea Sorbi
Stanislaw Bereznyuk
Affiliation:
Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia, E-mail: stas@cclib.nsu.ru
Richard Coles
Affiliation:
Mathematics Department, Victoria University of Wellington, Wellington, New Zealand, E-mail: coles@cs.auckland.ac.nz Department of Computer Science, University of Auckland, Auckland, New Zealand, E-mail: coles@cs.auckland.ac.nz
Andrea Sorbi
Affiliation:
Department of Mathematics, University of Siena, Siena, Italy, E-mail: sorbi@unisi.it
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that for every enumeration degree a < 0′e there exists an e-degree c such that a ≤ c < 0′e, and all degrees b, with c ≤ b < 0′e, are properly Σ20.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 19 - 32
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Calhoun, W. C. and Slaman, T. A., The Π21 e-degrees are not dense, this Journal, vol. 61 (1996), pp. 1364–1379.Google Scholar
[2]Cooper, S. B., Partial degrees and the density problem. Part 2: The enumeration degrees of the 2 sets are dense, this Journal, vol. 49 (1984), pp. 503–513.Google Scholar
[3]Cooper, S. B., Enumeration reducibility, nondeterministic computations and relative computability of partial functions, Recursion theory week, Oberwolfach 1989 (Ambos-Spies, K., MÜller, G., and Sacks, G. E., editors), Lecture Notes in Mathematics, no. 1432, Springer-Verlag, Heidelberg, 1990, pp. 57–110.Google Scholar
[4]Cooper, S. B. and Copestake, C. S., Properly 2 enumeration degrees, Zeitschrift fÜr Mathematische Logik und Grundlagen der Mathematik, vol. 34 (1988), pp. 491–522.CrossRefGoogle Scholar
[5]McEvoy, K., Jumps of quasi-minimal enumeration degrees, this Journal, vol. 50 (1985), pp. 839–848.Google Scholar
[6]McEvoy, K. and Cooper, S. B., On minimal pairs of enumeration degrees, this Journal, vol. 50 (1985), pp. 983–1001.Google Scholar
[7]Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar
[8]Shoenfield, J. R., On degrees of unsolvability, Annals of Mathematics, vol. 69 (1959), pp. 644–653.CrossRefGoogle Scholar
[9]Sorbi, A., The enumeration degrees of the 20 sets, Complexity, logic and recursion theory (Sorbi, A., editor), Marcel Dekker, New York, 1997, pp. 303–330.Google Scholar