Gödel’s incompleteness theorems
Se ha publicado un artículo de razonamiento aproximado en Isabelle/HOL sobre metalógica titulado Gödel’s incompleteness theorems.
Su autor es Lawrence C. Paulson (de la Universidad de Cambridge).
Su resumen es
Gödel’s two incompleteness theorems are formalised, following a careful presentation by Swierczkowski, in the theory of hereditarily finite sets. This represents the first ever machine-assisted proof of the second incompleteness theorem. Compared with traditional formalisations using Peano arithmetic (see e.g. Boolos), coding is simpler, with no need to formalise the notion of multiplication (let alone that of a prime number) in the formalised calculus upon which the theorem is based. However, other technical problems had to be solved in order to complete the argument.
El trabajo se ha publicado en The Archive of Formal Proofs
El código de las correspondientes teorías en Isabelle/HOL se encuentra aquí.