Jumping to a Uniform Upper Bound
Copyright policy )Jumping to a Uniform Upper Bound
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 .
join, jump, Other degrees and reducibilities in computability and recursion theory, uniform upper bound, ideal in the semi-lattice of Turing degrees, Hierarchies of computability and definability
join, jump, Other degrees and reducibilities in computability and recursion theory, uniform upper bound, ideal in the semi-lattice of Turing degrees, Hierarchies of computability and definability
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