Order‐free Recursion on the Real Numbers
Vasco Brattka · Mathematical logic quarterly · 1997
Abstract We investigate operations, computable in the sense of Recursive Analysis, which can be generated recursively from the arithmetic operations and the limit operation without using any tests on the real numbers. These functions, called order‐free recursive, can be shown to include a large class of computable functions. As main tools we provide an effective version of the Stone‐Weierstraß Approximation Theorem, as well as recursive partitions of unity.