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June 2002 A General Notion of Realizability
Lars Birkedal
Bull. Symbolic Logic 8(2): 266-282 (June 2002). DOI: 10.2178/bsl/1182353873

Abstract

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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Lars Birkedal. "A General Notion of Realizability." Bull. Symbolic Logic 8 (2) 266 - 282, June 2002. https://doi.org/10.2178/bsl/1182353873

Information

Published: June 2002
First available in Project Euclid: 20 June 2007

zbMATH: 1031.03080
MathSciNet: MR1919591
Digital Object Identifier: 10.2178/bsl/1182353873

Rights: Copyright © 2002 Association for Symbolic Logic

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Vol.8 • No. 2 • June 2002
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