Publisher's Synopsis
This work is a comprehensive introduction to an intrinsic algebraic-axiomatic study of recursion theory, an important branch of mathematical logic with applications in computer science. It aims to advance a better understanding of logic and mathematics, offering a framework which unifies many diverse notations in a lucid straightforward way.;The mathematical core of the work is the theory of a specially-designed algebraic system, operative space, which relates to effective compatibility as groups relate to symmetry. In addition to formulating a number of new results, the work includes more general versions of classical theorems, furnishing them with purely algebraic proofs. The author uses appropriate spaces to achieve index-free descriptions of particular notations of effective compatibility, paving the way for conceptual and practical applications of the general theory.