Cardinals in Isabelle/HOL

Blanchette, Jasmin Christian, Popescu, Andrei and Taytel, Dmitriy (2014) Cardinals in Isabelle/HOL. Interactive Theorem Proving: 5th International Conference, ITP 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 14-17, 2014. Proceedings. In: 5th International Conference on Interactive Theorem Proving, 14-17 Jul 2014, Vienna, Austria. ISBN 9783319089690. ISSN 0302-9743 [Conference or Workshop Item]

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Abstract

We report on a formalization of ordinals and cardinals in Isabelle/HOL. A main challenge we faced was 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 identifying ordinals with well-orders, with all concepts and results proved to be invariant under order isomorphism. We also discuss several applications of this general theory in formal developments.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published paper appears in: Interactive Theorem Proving, Volume 8558 of the series Lecture Notes in Computer Science pp 111-127, 2014
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 15164
Notes on copyright: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-08970-6_8
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Depositing User: Andrei Popescu
Date Deposited: 23 Apr 2015 09:17
Last Modified: 09 Jun 2021 17:30
URI: https://eprints.mdx.ac.uk/id/eprint/15164

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