一句话：在不使用无穷名称的情况下，给出条件可计算实函数的表征定理。
论文研究实函数的可计算性。相对于一个较小的次递归算子类，一致可计算实函数能在定义域的紧子集上计算微积分中的初等函数；条件可计算实函数是该类的真扩展，并能在整个定义域上计算这些初等函数。两类定义均依赖实数无穷名称的某种变换。本文沿用 Tent 与 Ziegler 的思路，在不使用无穷名称的条件下刻画条件可计算性，从而给出条件可计算实函数的一个新表征。
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.
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@article{Georgiev17,
title = {Characterization theorem for the conditionally computable real functions},
author = {Ivan Georgiev},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 3},
year = {2017},
doi = {10.23638/lmcs-13(3:3)2017}
}