Reseña: Cardinals in Isabelle/HOL

Se ha publicado un artículo de razonamiento formalizado en Isabelle/HOL sobre teoría de conjuntos titulado Cardinals in Isabelle/HOL.

Sus autores son Jasmin Christian Blanchette, Andrei Popescu y Dmitriy Traytel (de la Univ. Técnica de Munich).

Su resumen es

We report on a formalization of ordinals and cardinals in Isabelle/HOL. A main challenge we faced is the inability of higher-order logic to represent ordinals canonically, as transitive sets (as done in set theory). We resolved this into a “decentralized” representation that identifies ordinals with wellorders, with all concepts and results proved to be invariant under order isomorphism. We also discuss two applications of this general theory in formal developments.

El trabajo se presentará el martes 15 de julio en el ITP 2014 (5th Conference on Interactive Theorem Proving).