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A set with barely degree

Published online by Cambridge University Press:  12 March 2014

Rod Downey ,
Geoffrey Laforte  and
Steffen Lempp
Rod Downey
Affiliation:
School of Mathematical and Computer Sciences, Victoria University, Po Box 600, Wellington, New Zealand, E-mail: [email protected]
Geoffrey Laforte
Affiliation:
Institute For Human and Machine Cognition, 11000 University Parkway, Pensacola. FL 32514, USA, E-mail: [email protected]
Steffen Lempp
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706-1388, USA, E-mail: [email protected]
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Abstract

We construct a degree which fails to be computably enumerable in any computably enumerable set strictly below .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1700 - 1718
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Arslanov, M., LaForte, G., and Slaman, T., Relative enumerability in the difference hierarchy, this Journal.Google Scholar
[2]Downey, R., The 0‴ priority method with special attention to density results, Recursion theory week: Proceedings, Oberwohlfach 1989 (Ambos-Spies, K.et al., editors), Springer, Berlin, 1990.Google Scholar
[3]Sacks, G., Recursive enumerability and the jump operator, Transactions of the American Mathematical Society, vol. 108 (1963), pp. 223–239.CrossRefGoogle Scholar
[4]Shore, R., A non-inversion theorem for the jump operator, Annals of Pure and Applied Logic, vol. 40 (1988), pp. 277–303.CrossRefGoogle Scholar
[5]Soare, R., Recursively enumerable sets and degrees, Springer, Berlin, 1987.CrossRefGoogle Scholar