The generalised type-theoretic interpretation of constructive set theory

@article{Aczel2006TheGT,
  title={The generalised type-theoretic interpretation of constructive set theory},
  author={Peter Aczel and Nicola Gambino},
  journal={J. Symb. Log.},
  year={2006},
  volume={71},
  pages={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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Intuitionistic Type Theory — Notes by G

  • P. Martin-Löf
  • Sambin of a series of lectures given in Padua…
  • 1984
Highly Influential
15 Excerpts

Martin-Löf Type Theory

  • B. Nordström, K. Petersson, J. M. Smith
  • S. Abramski, D. M. Gabbay, and T. S. E. Maibaum…
  • 2000
Highly Influential
12 Excerpts

Towards a minimalistic foundation for constructive mathematics

  • M. E. Maietti, G. Sambin
  • L. Crosilla and P. Schuster, editors, From Sets…
  • 2005
1 Excerpt

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