Cardinals in Isabelle/HOL

  • Jasmin Christian Blanchette
  • Andrei Popescu
  • Dmitriy Traytel
Conference paper

DOI: 10.1007/978-3-319-08970-6_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8558)
Cite this paper as:
Blanchette J.C., Popescu A., Traytel D. (2014) Cardinals in Isabelle/HOL. In: Klein G., Gamboa R. (eds) Interactive Theorem Proving. ITP 2014. Lecture Notes in Computer Science, vol 8558. Springer, Cham

Abstract

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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jasmin Christian Blanchette
    • 1
  • Andrei Popescu
    • 1
    • 2
  • Dmitriy Traytel
    • 1
  1. 1.Fakultät für InformatikTechnische Universität MünchenGermany
  2. 2.Institute of Mathematics Simion Stoilow of the Romanian AcademyBucharestRomania

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