On the computational content of the axiom of choice

Stefano Berardi, Marc Bezem, Thierry Coquand
1998 Journal of Symbolic Logic (JSL)  
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
more » ... the one based on Gödel's Dialectica interpretation.
doi:10.2307/2586854 fatcat:zpaddcad75hmjo5vxzxycusnaq