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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Aczel, Peter 2013. Rudimentary and arithmetical constructive set theory. Annals of Pure and Applied Logic, Vol. 164, Issue. 4, p. 396.


    ADAMS, ROBIN and LUO, ZHAOHUI 2011. A pluralist approach to the formalisation of mathematics. Mathematical Structures in Computer Science, Vol. 21, Issue. 04, p. 913.


    Adams, Robin and Luo, Zhaohui 2010. Classical predicative logic-enriched type theories. Annals of Pure and Applied Logic, Vol. 161, Issue. 11, p. 1315.


    Maietti, Maria Emilia 2009. A minimalist two-level foundation for constructive mathematics. Annals of Pure and Applied Logic, Vol. 160, Issue. 3, p. 319.


    Gambino, Nicola 2008. The associated sheaf functor theorem in algebraic set theory. Annals of Pure and Applied Logic, Vol. 156, Issue. 1, p. 68.


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The generalised type-theoretic interpretation of constructive set theory

  • Nicola Gambino (a1) and Peter Aczel (a2)
  • DOI: http://dx.doi.org/10.2178/jsl/1140641163
  • Published online: 01 March 2014
Abstract
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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