Cardinals in Isabelle/HOL

Jasmin Christian Blanchette, Andrei Popescu, Dmitriy Traytel


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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Paper draft