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ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS

Published online by Cambridge University Press:  15 May 2017

RUTGER KUYPER*
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICSVICTORIA UNIVERSITY OF WELLINGTONPO BOX 600, WELLINGTON 6140NEW ZEALANDE-mail: mail@rutgerkuyper.com

Abstract

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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2017 

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