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
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 is a uniform upper bound on an ideal of degrees then is the jump of a degree with this additional property: there is a uniform bound so that .
-  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 0360242, https://doi.org/10.2307/2272899
- H. Hodes, More on uniform upper bounds, J. Symbolic Logic (to appear).
- H. Rogers, The theory of recursive functions and effective computability, McGraw-Hill, New York, 1967. MR 0224462 (37:61)
- L. Sasso, A minimal degree not realizing least possible jump, J. Symbolic Logic 39 (1974). MR 0360242 (50:12692)
Keywords: Turing, degree, jump, ideal, uniform upper bound, tree
Article copyright: © Copyright 1982 American Mathematical Society