The Peirce translation and the double negation shift

Authors:
Martín Escardó;Paulo Oliva
Affiliations:
School of Computer Science, University of Birmingham, Birmingham, United Kingdom;School of Electronic Engineering and Computer Science, Queen Mary, University of London, London, United Kingdom
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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Abstract

We develop applications of selection functions to proof theory and computational extraction of witnesses from proofs in classical analysis. The main novelty is a translation of classical minimal logic into minimal logic, which we refer to as the Peirce translation, and which we apply to interpret both a strengthening of the double-negation shift and the axioms of countable and dependent choice, via infinite products of selection functions.