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Journal of Symbolic Logic
Article . 1998 . Peer-reviewed
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Article . 1998
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On the computational content of the axiom of choice

Authors: Berardi, Stefano; Bezem, Marc; Coquand, Thierry;

On the computational content of the axiom of choice

Abstract

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.

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
55
Top 10%
Top 10%
Average
Green
bronze