Journal of Symbolic Logic

On the Computational Content of the Axiom of Choice

Stefano Berardi, Marc Bezem, and Thierry Coquand

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We present a possible computational content of the negative translation of classical analysis with the Axiom of (countable) Choice. Interestingly, this interpretation uses a refinement of the realizability 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 of $\exists$-statements and how to extract algorithms from proofs of $\forall\exists$-statements. Our interpretation seems computationally more direct than the one based on Godel's Dialectica interpretation.

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J. Symbolic Logic, Volume 63, Issue 2 (1998), 600-622.

First available in Project Euclid: 6 July 2007

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Berardi, Stefano; Bezem, Marc; Coquand, Thierry. On the Computational Content of the Axiom of Choice. J. Symbolic Logic 63 (1998), no. 2, 600--622.

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