2001/04/02 by Jailton C. Ferreira, Ferreira, Jailton C.
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #DNA and Biological Computing #Data Management and Algorithms #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.math/0104025
openalex publication_date 2001/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.