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The degrees of hyperhyperimmune sets1

Published online by Cambridge University Press:  12 March 2014

Carl G. Jockusch Jr.
Carl G. Jockusch Jr.*
Affiliation:
University of Illinois
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Extract

In [5, Corollary 3.1] D. A. Martin characterized the degrees of the hyperhypersimple sets as those r.e. degrees a satisfying a′ = 0″. In the present paper we investigate the degrees of the hyperhyperimmune (h.h.i.) sets. We do not achieve a characterization of these degrees, but we do show that the condition a′ ≥ 0″ is sufficient, and the condition a′ ≥ 0′ is necessary, for a degree a to contain an h.h.i. set.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 489 - 493
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

This research was supported by National Science Foundation grant GP 7421.

References

[1]Dekker, J. C. E. and Myhill, J., Recursive equivalence types, University of California publications in mathematics, vol. 3 (1960), pp. 67–213.Google Scholar
[2]Dekker, J. C. E. and Myhill, J., Retraceable sets, Canadian Journal of Mathematics, vol. 10 (1958), pp. 357–373.CrossRefGoogle Scholar
[3]Feferman, S., Some applications of the notion of forcing and generic sets, Fundamenta mathematicae, vol. 56 (1965), pp. 325–345.CrossRefGoogle Scholar
[4]Jockusch, C. G. Jr. and McLaughlin, T. G., Countable retracing functions and Π20predicates, Pacific journal of mathematics (to appear).Google Scholar
[5]Martin, D. A., Classes of recursively enumerable sets and degrees of unsolvability, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 12 (1966), pp. 295–310.CrossRefGoogle Scholar
[6]Martin, D. A., A theorem on hyperhypersimple sets, this Journal, vol. 28 (1963), pp. 273–278.Google Scholar
[7]Miller, W. and Martin, D. A., The degrees of hyperimmune sets, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 14 (1968), pp. 159–166.CrossRefGoogle Scholar
[8]Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar
[9]Sacks, G., Degrees of unsolvability, Annals of mathematics studies, no. 55, Princeton Univ. Press, Princeton, N.J., 1963.Google Scholar
[10]Shoenfield, J. R., On degrees of unsolvability, Annals of mathematics, vol. 69 (1959), pp. 644–653.CrossRefGoogle Scholar
[11]Shoenfield, J.R., A theoremon minimal degrees, this Journal, vol. 31 (1966), pp. 539–544.Google Scholar
[12]Yates, C. E. M., Recursively enumerable sets and retracing functions, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), pp. 331–345.CrossRefGoogle Scholar