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The generalised type-theoretic interpretation of constructive set theory

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journal contribution
posted on 08.12.2009, 16:13 by Nicola Gambino, Peter Aczel
We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive. The primitive treatment of logic in type theories allows us to study reinterpretations of logic, such as the double-negation translation.

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Citation

Journal of Symbolic Logic, 2006, 71 (1), pp.67-103

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VoR (Version of Record)

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Journal of Symbolic Logic

Publisher

Association for Symbolic Logic

issn

0022-4812

Copyright date

2006

Available date

08/12/2009

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http://projecteuclid.org/euclid.jsl/1140641163

Language

en

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