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A General Notion of Realizability

Published online by Cambridge University Press:  15 January 2014

Lars Birkedal
Lars Birkedal*
Affiliation:
The IT University of Copenhagen, Glentevej 67, DK–2400 Copenhagen NV, DenmarkE-mail: birkedal@itu.dk
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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 show 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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 8 , Issue 2 , June 2002 , pp. 266 - 282
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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