1. Nicola Gambino (2008). The Associated Sheaf Functor Theorem in Algebraic Set Theory. Annals of Pure and Applied Logic 156 (1):68-77.
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  2. Nicola Gambino (2006). Heyting-Valued Interpretations for Constructive Set Theory. Annals of Pure and Applied Logic 137 (1):164-188.
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  3. Nicola Gambino & Peter Aczel (2006). The Generalised Type-Theoretic Interpretation of Constructive Set Theory. Journal of Symbolic Logic 71 (1):67 - 103.
    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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