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• W3149538277 abstract "Abst rac t . We present two mutual encodings, respectively of the Calculus of Inductive Constructions in Zermelo-Fraenkel set theory and the opposite way. More precisely, we actually construct two families of encodings, relating the number of universes in the type theory with the number of inaccessible cardinals in the set theory. The main result is that both hierarchies of logical formalisms interleave w.r.t, expressive power and thus are essentially equivalent. Both encodings are quite elementary: type theory is interpreted in set theory through a generalization of Coquand's simple proof-irrelevance interpretation. Set theory is encoded in type theory using a variant of Aczel's encoding; we have formally checked this last part using the Coq proof assistant." @default.
• W3149538277 created "2021-04-13" @default.
• W3149538277 creator A5064352619 @default.
• W3149538277 date "2005-01-01" @default.
• W3149538277 modified "2023-09-27" @default.
• W3149538277 title "Sets in Types , Types in Sets" @default.
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