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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Jumping to a uniform upper bound
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by Harold Hodes PDF
Proc. Amer. Math. Soc. 85 (1982), 600-602 Request permission

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 $\underline b \vee \underline c < \underline a$.
References
    H. Hodes, More on uniform upper bounds, J. Symbolic Logic (to appear).
  • Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
  • Leonard P. Sasso Jr., A minimal degree not realizing least possible jump, J. Symbolic Logic 39 (1974), 571–574. MR 360242, DOI 10.2307/2272899
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 600-602
  • MSC: Primary 03D30; Secondary 03D55
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0660612-6
  • MathSciNet review: 660612