We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than what a related study by Giusto, Brown, and Simpson has revealed in the setting of reverse mathematics. In particular, different formulations of the Vitali Covering Theorem turn out to have different uniform computational content. These versions are either computable or closely related to uniform variants of Weak Weak König’s Lemma.

Vasco Brattka, Guido Gherardi, Rupert Hölzl, Arno Pauly (2017). The Vitali Covering Theorem in the Weihrauch Lattice. Cham : Springer [10.1007/978-3-319-50062-1_14].

The Vitali Covering Theorem in the Weihrauch Lattice

GHERARDI, GUIDO;
2017

Abstract

We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than what a related study by Giusto, Brown, and Simpson has revealed in the setting of reverse mathematics. In particular, different formulations of the Vitali Covering Theorem turn out to have different uniform computational content. These versions are either computable or closely related to uniform variants of Weak Weak König’s Lemma.
2017
Computability and Complexity
188
200
Vasco Brattka, Guido Gherardi, Rupert Hölzl, Arno Pauly (2017). The Vitali Covering Theorem in the Weihrauch Lattice. Cham : Springer [10.1007/978-3-319-50062-1_14].
Vasco Brattka; Guido Gherardi; Rupert Hölzl; Arno Pauly
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/577646
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