The generalised type-theoretic interpretation of constructive set theory

@article{Aczel2006TheGT,
  title={The generalised type-theoretic interpretation of constructive set theory},
  author={P. Aczel and N. Gambino},
  journal={J. Symb. Log.},
  year={2006},
  volume={71},
  pages={67-103}
}
  • P. Aczel, N. Gambino
  • Published 2006
  • Computer Science, Mathematics
  • J. Symb. Log.
  • We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Ltype theory. The original interpretation treated logic in Martin-Ltype theory viathe propositions-as-types interpretation. The generalisation involves replacing Martin-L¨ of type theory with anew type theory inwhichlogicistreated asprimitive. Theprimitive treatment oflogicintype theories allowsustostudyreinterpretations oflogic,suchasthedouble-negationtranslation. Introduction. Thetype… CONTINUE READING
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