On Weihrauch Reducibility and Intuitionistic Reverse Mathematics
Rutger Kuyper
TL;DR
This paper explores the relationship between Weihrauch reducibility and provability in an intuitionistic framework, revealing how certain reducibility notions correspond to provability in specific logical systems.
Contribution
It establishes a formal connection between Weihrauch reducibility and provability in EL_0 with Markov's principle, clarifying their logical correspondence.
Findings
Weihrauch reducibility to finitely many instances corresponds to provability in EL_0 with Markov's principle.
Weihrauch reducibility is characterized by an affine subsystem of EL_0 plus Markov's principle.
The work bridges computability notions with intuitionistic proof systems.
Abstract
We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL_0, the intuitionistic version of RCA_0, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL_0 together with Markov's principle, and that Weihrauch reducibility is captured by an affine subsystem of EL_0 plus Markov's principle.
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