Typed realizability for first-order classical analysis

  title={Typed realizability for first-order classical analysis},
  author={Valentin Blot},
  journal={Log. Methods Comput. Sci.},
  • Valentin Blot
  • Published 16 December 2015
  • Computer Science
  • Log. Methods Comput. Sci.
We describe a realizability framework for classical first-order logic in which realizers live in (a model of) typed {\lambda}{\mu}-calculus. This allows a direct interpretation of classical proofs, avoiding the usual negative translation to intuitionistic logic. We prove that the usual terms of G\"odel's system T realize the axioms of Peano arithmetic, and that under some assumptions on the computational model, the bar recursion operator realizes the axiom of dependent choice. We also perform a… 

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