Cardinals in Isabelle/HOL

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8558)


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.


Regular Cardinal Order Isomorphism Strict Partial Order Initial Algebra Witness Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Fakultät für InformatikTechnische Universität MünchenGermany
  2. 2.Institute of Mathematics Simion Stoilow of the Romanian AcademyBucharestRomania

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