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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Jumping to a uniform upper bound


Author: Harold Hodes
Journal: Proc. Amer. Math. Soc. 85 (1982), 600-602
MSC: Primary 03D30; Secondary 03D55
MathSciNet review: 660612
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Abstract: A uniform upper bound on a class of Turing degrees is the Turing degree of a function which parametrizes the collection of all functions whose degree is in the given class. I prove that if $ \underline a $ is a uniform upper bound on an ideal of degrees then $ \underline a $ is the jump of a degree $ \underline c $ with this additional property: there is a uniform bound $ \underline b < \underline a $ so that $ \underline b \vee \underline c < \underline a $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660612-6
PII: S 0002-9939(1982)0660612-6
Keywords: Turing, degree, jump, ideal, uniform upper bound, tree
Article copyright: © Copyright 1982 American Mathematical Society