Bulletin of Symbolic Logic

A General Notion of Realizability

Lars Birkedal

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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.

Article information

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

Dates
First available in Project Euclid: 20 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1182353873

Digital Object Identifier
doi:10.2178/bsl/1182353873

Mathematical Reviews number (MathSciNet)
MR1919591

Zentralblatt MATH identifier
1031.03080

JSTOR
links.jstor.org

Citation

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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