
doi: 10.2307/2586854
AbstractWe 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 Gödel's Dialectica interpretation.
intuitionistic arithmetic, higher-order functionals, Axiom of choice and related propositions, Metamathematics of constructive systems, Intuitionistic mathematics, Wijsbegeerte, axiom of choice, functional interpretation of classical analysis, excluded middle
intuitionistic arithmetic, higher-order functionals, Axiom of choice and related propositions, Metamathematics of constructive systems, Intuitionistic mathematics, Wijsbegeerte, axiom of choice, functional interpretation of classical analysis, excluded middle
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