Characterization theorem for the conditionally computable real functions

The class of uniformly computable real functions with respect to a smallsubrecursive class of operators computes the elementary functions of calculus,restricted to compact subsets of their domains. The class of conditionallycomputable real functions with respect to the same class of operators is aproper extension of the class of uniformly computable real functions and itcomputes the elementary functions of calculus on their whole domains. Thedefinition of both classes relies on certain transformations of infinitisticnames of real numbers. In the present paper, the conditional computability ofreal functions is characterized in the spirit of Tent and Ziegler, avoiding theuse of infinitistic names