Jumping to a uniform upper bound
Harold T. Hodes · Proceedings of the American Mathematical Society · 1982
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 a _ \underline a is a uniform upper bound on an ideal of degrees then a _ \underline a is the jump of a degree c _ \underline c with this additional property: there is a uniform bound b _ > a _ \underline b > \underline a so that b _ ∨ c _ > a _ \underline b \vee \underline c > \underline a .