Bulletin of Symbolic Logic

A General Notion of Realizability

Lars Birkedal

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We present a general notion of realizability encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial cartesian closed categories. We shown how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result) that the category Equ of equilogical spaces models dependent predicate logic. Moreover, we characterize when the general notion of realizability gives rise to a topos, i.e., a model of impredicative intuitionistic higher-order logic.

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Bull. Symbolic Logic, Volume 8, Number 2 (2002), 266-282.

First available in Project Euclid: 20 June 2007

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Birkedal, Lars. A General Notion of Realizability. Bull. Symbolic Logic 8 (2002), no. 2, 266--282. doi:10.2178/bsl/1182353873. https://projecteuclid.org/euclid.bsl/1182353873

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