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Jumping to a uniform upper bound


Author: Harold Hodes
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
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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 $.


References [Enhancements On Off] (What's this?)

  • [1] H. Hodes, More on uniform upper bounds, J. Symbolic Logic (to appear).
  • [2] H. Rogers, The theory of recursive functions and effective computability, McGraw-Hill, New York, 1967. MR 0224462 (37:61)
  • [3] L. Sasso, A minimal degree not realizing least possible jump, J. Symbolic Logic 39 (1974). MR 0360242 (50:12692)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0660612-6
Keywords: Turing, degree, jump, ideal, uniform upper bound, tree
Article copyright: © Copyright 1982 American Mathematical Society

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