A realization of the negative interpretation of the Axiom of Choice

  • Stefano Berardi
  • Marc Bezem
  • Thierry Coquand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 902)


We present a possible computational content of the negative translation of classical analysis with the Axiom of Choice. Interestingly, this interpretation uses a refinement of the realizibility semantics of the absurdity proposition, which is not interpreted as the empty type here. We also show how to compute witnesses from proofs in classical analysis, and how to extract algorithms from proofs of ∀∃ statements.


Classical Logic Axiom Schema Negative Interpretation Realizability Interpretation Lambda Abstraction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Stefano Berardi
    • 1
  • Marc Bezem
    • 2
  • Thierry Coquand
    • 3
  1. 1.Dip. InformaticaChalmers Torino UniversityTorinoItaly
  2. 2.Department of PhilosophyUtrecht UniversityTC UtrechtThe Netherlands
  3. 3.Department of Computer SciencesChalmers University of GothenburgGothenburgSweden

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