The Generalised Type-Theoretic Interpretation of Constructive Set Theory

Journal of Symbolic Logic 71 (1):67 - 103 (2006)
Abstract
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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Citations of this work BETA
Peter Aczel (2013). Rudimentary and Arithmetical Constructive Set Theory. Annals of Pure and Applied Logic 164 (4):396-415.
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