recursive function theory a relatively recent area of mathematics that takes as its point of departure the study of an extremely limited class of arithmetic functions called the recursive functions. Strictly speaking, recursive function theory is a branch of higher arithmetic (number theory, or the theory of natural numbers) whose universe of discourse is restricted to the nonnegative integers: 0, 1, 2, etc. However, the techniques and results of the newer area do not resemble those traditionally associated with number theory. The class of recursive functions is defined in a way that makes evident that every recursive function can be computed or calculated. The hypothesis that every calculable function is recursive, which is known as Church’s thesis, is often taken as a kind of axiom in recursive function theory. This theory has played an important role in modern philosophy of mathematics, especially when epistemological issues are studied. See also CHURCH’S THESIS, COM- PUTABILITY , PHILOSOPHY OF MATHEMATICS , PROOF BY RECURSIO. J.Cor.