A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets

Se ha publicado un artículo de razonamiento formalizado en Isabelle titulado A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets.

Su autor es Lawrence C. Paulson (de la Universidad de Cambridge).

Su resumen es

A formalisation of Göodel’s incompleteness theorems using the Isabelle proof assistant is described. This is apparently the first mechanical verification of the second incompleteness theorem. The work closely follows Świerczkowski (2003), who gave a detailed proof using hereditarily finite set theory. The adoption of HF is generally beneficial, but it poses certain technical issues that do not arise for Peano arithmetic. The formalisation itself should be useful to logicians, particularly concerning the second incompleteness theorem, where existing proofs are lacking in detail.