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 is a uniform upper bound on an ideal of degrees then a is the jump of a degree c with this additional property: there is a uniform bound b<a so that b V c < a.
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M. Lerman (1985). Upper Bounds for the Arithmetical Degrees. Annals of Pure and Applied Logic 29 (3):225-254.

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