Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
  • [3] Leonard P. Sasso Jr., A minimal degree not realizing least possible jump, J. Symbolic Logic 39 (1974), 571–574. MR 0360242

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03D30, 03D55

Retrieve articles in all journals with MSC: 03D30, 03D55

Additional Information

Keywords: Turing, degree, jump, ideal, uniform upper bound, tree
Article copyright: © Copyright 1982 American Mathematical Society