On the computational content of the axiom of choice

Journal of Symbolic Logic 63 (2):600-622 (1998)
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 ∃-statements and how to extract algorithms from proofs of ∀∃-statements. Our interpretation seems computationally more direct than the one based on Godel's Dialectica interpretation
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DOI 10.2307/2586854
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Ulrich Berger (2005). Uniform Heyting Arithmetic. Annals of Pure and Applied Logic 133 (1):125-148.
Martín Escardó & Paulo Oliva (2012). The Peirce Translation. Annals of Pure and Applied Logic 163 (6):681-692.
Thomas Powell (2014). The Equivalence of Bar Recursion and Open Recursion. Annals of Pure and Applied Logic 165 (11):1727-1754.
Klaus Aehlig (2008). Parameter-Free Polymorphic Types. Annals of Pure and Applied Logic 156 (1):3-12.

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