Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-31T19:09:25.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Regular enumerations

Published online by Cambridge University Press:  12 March 2014

I. N. Soskov  and
V. Baleva
I. N. Soskov
Affiliation:
Sofia University, Faculty of Mathematics and Computer Science, Blvd. “James Bourchier” 5, 1164 Sofia, Bulgaria, E-mail: [email protected]
V. Baleva
Affiliation:
Sofia University, Faculty of Mathematics and Computer Science, Blvd. “James Bourchier” 5, 1164 Sofia, Bulgaria, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In the paper we introduce and study regular enumerations for arbitrary recursive ordinals. Several applications of the technique are presented.

Keywords

03D30Enumeration reducibilityEnumeration jumpEnumeration degrees
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1323 - 1343
Copyright
Copyright © Association for Symbolic Logic 2002

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]Ash, C. J., Generalizations of enumeration reducibility using recursive infinitary propositional sentences, Annals of Pure and Applied Logic, vol. 58 (1992), pp. 173–184.CrossRefGoogle Scholar
[2]Ash, C. J., Jockush, C., and Knight, J. F., Jumps of orderings, Transactions of the American Mathematical Society, vol. 319 (1990), pp. 573–599.CrossRefGoogle Scholar
[3]Case, J., Maximal arithmetical reducibilities, Zeitschrift für Mathematische Logik and Grundlagen der Mathematik, vol. 20 (1974), pp. 261–270.CrossRefGoogle Scholar
[4]Coles, R., Downey, R., and Slaman, T., Every set has a least jump enumeration, Bulletin of the London Mathematical Society, to appear.Google Scholar
[5]Cooper, S. B., Partial degrees and the density problem. Part 2: The enumeration degrees of the Σ2 sets are dense, this Journal, vol. 49 (1984), pp. 503–513.Google Scholar
[6]Cooper, S. B., Enumeration reducibility, nondeterministic computations and relative computability of partial functions, Recursion Theory Week, Oberwolfach 1989 (Sacks, G. E., Ambos-Spies, K., and Muler, G., editors), Lecture Notes in Mathematics, vol. 1432, Springer-Verlag, Heidelberg, 1990, pp. 57–110.Google Scholar
[7]Copestake, K., 1-Genericity in the enumeration degrees, this Journal, vol. 53 (1988), pp. 878–887.Google Scholar
[8]Downey, R. G. and Knight, J. F., Orderings with α-th jump degree 0(α), Proceedings of the American Mathematical Society, vol. 114, 1992, pp. 545–552.Google Scholar
[9]McEvoy, K., Jumps of quasi-minimal enumeration degrees, this Journal, vol. 50 (1985), pp. 839–848.Google Scholar
[10]Rogers, H. Jr, Theory of recursive functions and effective computability, McGraw-Hill Book Company, New York, 1967.Google Scholar
[11]Sacks, G. E., Higher Recursion Theory, Springer-Verlag, Berlin, Heidelberg, New York, London, 1990.CrossRefGoogle Scholar
[12]Selman, A. L., Arithmetical reducibilities I, Zeitschrift för Mathematische Logik und Grundlagen der Mathematik, vol. 17 (1971), pp. 335–350.CrossRefGoogle Scholar
[13]Soskov, I. N., A jump inversion theorem for the enumeration jump, Archive for Mathematical Logic, vol. 39 (2000), pp. 417–437.CrossRefGoogle Scholar