On the connection between the abstract recursion theory and the method of successive approximations

Abstract

We introduce the concept of orthogonalizable semiring which contains as a special case some familiar objects of classical pure mathematics and, on the other hand, is fit for the purposes of the algrebraic recursion theory. A fundamental result of the last theory, called code evaluating theorem, is proved for such semirings. Some corollaries are considered, especially for the ring of bounded linear operators over a infinite dimensional Hilberd space.