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 $\underline b \vee \underline c < \underline a$.
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
- © 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