A General Notion of Realizability (2000)
| Venue: | In Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science |
| Citations: | 4 - 2 self |
BibTeX
@INPROCEEDINGS{Birkedal00ageneral,
author = {L. Birkedal},
title = {A General Notion of Realizability},
booktitle = {In Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science},
year = {2000},
pages = {7--17},
publisher = {IEEE Computer Society}
}
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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. 1. Introduction There has recently been a lot of interest in understanding how models based on realizability over partial combinatory algebras (PCAs) may be generalized to models based on realizability over more general structures [1, 3, 2, 18, 16, 15, 8]. For instance, in [3, 1] it is shown how how the category Equ of equilogical spaces can be thought of as a category of modest sets over the category of algebraic lattices and,...
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