ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS

ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS

We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL₀, the intuitionistic version of RCA₀, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provabili...

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Veröffentlicht in:The Journal of symbolic logic 2017-12, Vol.82 (4), p.1438-1458
1. Verfasser: KUYPER, RUTGER
Format: Artikel
Sprache:eng
Schlagworte:
Calculus
Mathematics
Theorems
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Zusammenfassung:We show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL₀, the intuitionistic version of RCA₀, 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 EL₀ together with Markov’s principle, and that Weihrauch reducibility is captured by an affine subsystem of EL₀ plus Markov’s principle.
ISSN:0022-4812
1943-5886
DOI:10.1017/jsl.2016.61