Día: 18 noviembre 2013

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.

Se ha publicado un artículo de razonamiento aproximado en Isabelle/HOL sobre la teoría de conjuntos titulado The hereditarily finite sets.

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

Su resumen es

The theory of hereditarily finite (HF) sets is formalised, following the development of Swierczkowski. An HF set is a finite collection of other HF sets; they enjoy an induction principle and satisfy all the axioms of ZF set theory apart from the axiom of infinity, which is negated. All constructions that are possible in ZF set theory (Cartesian products, disjoint sums, natural numbers, functions) without using infinite sets are possible here. The definition of addition for the HF sets follows Kirby.

This development forms the foundation for the Isabelle proof of Gödel’s incompleteness theorems, which has been formalised separately.

El trabajo se ha publicado en The Archive of Formal Proofs.

El código de las correspondientes teorías en Isabelle/HOL se encuentra aquí.