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March 2006 The generalised type-theoretic interpretation of constructive set theory
Peter Aczel, Nicola Gambino
J. Symbolic Logic 71(1): 67-103 (March 2006). DOI: 10.2178/jsl/1140641163

Abstract

We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive instead of being formulated via the propositions-as-types representation. 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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Peter Aczel. Nicola Gambino. "The generalised type-theoretic interpretation of constructive set theory." J. Symbolic Logic 71 (1) 67 - 103, March 2006. https://doi.org/10.2178/jsl/1140641163

Information

Published: March 2006
First available in Project Euclid: 22 February 2006

zbMATH: 1100.03052
MathSciNet: MR2210056
Digital Object Identifier: 10.2178/jsl/1140641163

Subjects:
Primary: 03F25, 03F50

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 1 • March 2006
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