A direct proof of Gödel's incompleteness theorem
ISSN: 0010-0757
Year of publication: 1986
Volume: 37
Fascicle: 1
Pages: 81-83
Type: Article
More publications in: Collectanea mathematica
Abstract
An unusual enumeration of partial recursive functions is defined starting from the equivalence between recursiveness and representability in Peano arithmetic. This allows us to obtain by a double diagonalization an undecidable formula expressing a property of Peano arithmetic, equivalent to its consistency.