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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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. https://doi.org/10.1007/978-3-319-08970-6_8
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DOI: https://doi.org/10.1007/978-3-319-08970-6_8
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