On the Goedel's formula

Abstract

The proof of Goedel's first incompleteness theorem includes the construction of an arithmetic formula G that represents the metamathematical statement: the formula G is not provable. This article examines the formula G (of Goedel). We demonstrated that there is no Goedel's number for the formula G if number of provable well formed formulae with one free variable is finite. If there is a non-finite number of provable propositions in the theory, then Goedel's formula also does not possess the Goedel's number.

arXiv comment4 pages. Section 3 rewritten