Low functions of reals

Abstract

We introduce a new notion of computable function on ${\mathbb{R}}^N$ and prove some basic properties. We give two applications, first a short proof of Yoshinaga's theorem that periods are \el (they are actually low). We also show that the low complex numbers form a algebraically closed field closed under exponentiation and some other special functions.

We have added a reference to a paper of E. Specker