The hereditarily finite sets
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.