Code evaluation in operative spaces with storage operation

Abstract

A concept of storage operation in an operative space is considered, which is closely related to Ivanov's concept of storing operation in such spaces. For operative spaces with storage operation a code evaluation theorem, implying almost all principal results of algebraic recursion theory for such spaces, is proved. As a special case these results are obtained for a generalized version of Skordev's theory of combinatory spaces, free from using constant.