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Degrees in Which the Recursive Sets are Uniformly Recursive

Published online by Cambridge University Press:  20 November 2018

Carl G. Jockusch Jr.
Carl G. Jockusch Jr.*
Affiliation:
University of Illinois, Urbana, Illinois
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One of the most fundamental and characteristic features of recursion theory is the fact that the recursive sets are not uniformly recursive. In this paper we consider the degrees a such that the recursive sets are uniformly of degree ≦a and characterize them by the condition a’ ≦ 0". A number of related results will be proved, and one of these will be combined with a theorem of Yates to show that there is no r.e. degree a < 0’ such that the r.e. sets of degree ≦a are uniformly of degree ≦a. This result and a generalization will be used to study the relationship between Turing and many-one reducibility on the r.e. sets.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1092 - 1099
Copyright
Copyright © Canadian Mathematical Society 1972

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