Class of algebras of primitive recursive functions

Abstract

In this paper Robinson's algebra is embedded in a countable class of algebras of primitive recursive functions. Each algebra of this class contains the operations of addition and composition of functions and also one of the operations ia which are defined as follows: g(x)= iaf(x) (a=0, 1, 2, ...) if g(x) satisfies the equations g(0)=a and g(x+1)=f[g(x)]. In this paper we study the properties possessed by all or almost all the algebras of this class.