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The Π20 enumeration degrees are not dense

Published online by Cambridge University Press:  12 March 2014

William C. Calhoun  and
Theodore A. Slaman
William C. Calhoun
Affiliation:
Department of Mathematics, Kalamazoo College, Kalamazoo, Michigan 49006, USA, E-mail: calhoun@kzoo.edu
Theodore A. Slaman
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637, USA, E-mail: ted@math.uchicago.edu
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Abstract

We show that the Π20 enumeration degrees are not dense. This answers a question posed by Cooper.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 4 , December 1996 , pp. 1364 - 1379
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Cooper, S. B., Partial degrees and the density problem I, this Journal, vol. 47 (1982), pp. 854–859.Google Scholar
[2]Cooper, S. B., Partial degrees and the density problem, Part 2: The enumeration degrees of the sets are dense, this Journal, vol. 49 (1984), pp. 503–513.Google Scholar
[3]Cooper, S. B., Enumeration reducibility, non-deterministic computations and relative computability of partial functions, Recursion theory week, Lecture Notes in Mathematics, no. 1432, Springer-Verlag, Berlin, 1989, pp. 57–110.Google Scholar
[4]Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.CrossRefGoogle Scholar