ABSTRACT
To define the authors' class of functions, the authors introduce a computing machine called the basic machine. It is an idealized machine in that it has infinitely much memory and never makes a mistake. Except for these features, it is about as simple as a computing machine can be. To use the machine, they insert a program in the program holder; put any desired numbers in the registers; and start the machine. At each step, the machine executes the instruction in the program whose number is in the counter at the beginning of the step, provided that there is such an instruction. The instructions are of three types. The first type has the format INCREASE Ri. When the machine executes this instruction, it increases the number in Ri by 1 and increases the number in the counter by 1. The third type has the format GO TO n, where n is the number of an instruction in the program.
