ABSTRACT

Conversely, any number can be written in a unique way as a series of letters. Some of these will be nonsensical, others will be meaningful statements which are not either theorems or axioms of the theory considered, finally we will have numbers which correspond to statements which are theorems. We denote the statement "xis the Godel number of a theorem" by P(x) and the statement "xis not the Gi:idel number of a theorem" by~ P(x).