Four Test Problems in Generalized Recursion Theory

Abstract

This chapter discusses four test problems in generalized recursion theory (GRT). All recursion theory is concerned with computations in which individuals are manipulated by some sort of abstract computing engine. However, the principle of parity demands that the computation be of approximately the same complexity as the individuals. This means in practice that a particular kind of recursion theory is often determined completely by its domain of individuals. For example, in classical recursion theory (CRT), the domain of individuals is ω and this fact dictates the nature of the computations. The relations among the four kinds of GRT as well as CRT are also explained in the chapter. The chapter also discusses the basic notions of recursion theory as they apply to each kind of GRT.