Formalisms For Describing Computable Functions and Related Entities

In this part we describe a number of new formalisms for expressing computable functions and related entities. The most important section is 1, the subject matter of which is fairly well understood. The other sections give formalisms which we hope will be useful in constructing computable functions and in proving theorems about them.

• Functions Computable in Terms of Given Base Functions
• Recursive Functions of the Integers
• Computable Functionals
• Non-Computable Functions and Functionals
• Ambiguous Functions
• Recursive Definitions of Sets