chapter  5
33 Pages

Elementary and Primitive Recursive Functions

The theorems on undefinability and incompleteness have so far been studied in abstracio, viz. for languages L, assumed to admit coding functions g j , gp gg , and for axiom systems G , assumed to make representable, or definable, certain functions and relations coded with help of these functions, such as as sub and ded. In the following Chapters, I shall choose the set N , in which to code the language L , to be the set w, and I shall study axiom systems G for (fragments of) arithmetic; for them I shall have to verify those assump­ tions to hold.