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Variations on Realizability: Realizing the Propositional Axiom of Choice (2000)
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| Venue: | Math. Structures Comput. Sci |
| Citations: | 1 - 0 self |
BibTeX
@ARTICLE{Hyland00variationson,
author = {J. M. E. Hyland},
title = {Variations on Realizability: Realizing the Propositional Axiom of Choice},
journal = {Math. Structures Comput. Sci},
year = {2000},
volume = {12}
}
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Abstract
Introduction 1.1 Historical background Early investigators of realizability were interested in metamathematical questions. In keeping with the traditions of the time they concentrated on interpretations of one formal system in another. They considered an ad hoc collection of increasingly ingenious interpretations mainly to establish consistency, independence and conservativity results. van Oosten's contribution to the Workshop (see van Oosten [56] and the extended account van Oosten [57]) gave inter alia an account of these concerns from a modern perspective. (One should also draw attention to realizability used to provide interpretations of Brouwer's theory of Choice Sequences. An early approach is in Kleene Vesley [28]; for modern work in the area consult Moschovakis [35], [36], [37].) In the early days of categorical logic one considered realizability as providing models for constructive mathematics; while the metamathematics could be retrieved by `coding' the mod
Keyphrases
propositional axiom early approach ingenious interpretation extended account van oosten choice sequence formal system area consult moschovakis inter alia historical background early investigator metamathematical question early day categorical logic constructive mathematics kleene vesley ad hoc collection modern work conservativity result van oosten modern perspective
