# Characterization theorem for the conditionally computable real functions

## TL;DR

This paper characterizes the class of conditionally computable real functions, extending uniformly computable functions, by providing a new characterization that avoids the use of infinitistic names.

## Contribution

It offers a new characterization of conditionally computable real functions without relying on infinitistic names, expanding understanding of their computational properties.

## Key findings

- Conditionally computable functions extend uniformly computable functions.
- The new characterization avoids the use of infinitistic names.
- Computes elementary functions on entire domains.

## Abstract

The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable real functions with respect to the same class of operators is a proper extension of the class of uniformly computable real functions and it computes the elementary functions of calculus on their whole domains. The definition of both classes relies on certain transformations of infinitistic names of real numbers. In the present paper, the conditional computability of real functions is characterized in the spirit of Tent and Ziegler, avoiding the use of infinitistic names.