Computability and Complexity pp 188-200

Part of the Lecture Notes in Computer Science book series (LNCS, volume 10010)

The Vitali Covering Theorem in the Weihrauch Lattice

  • Vasco Brattka
  • Guido Gherardi
  • Rupert Hölzl
  • Arno Pauly
Chapter

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 Kőnig’s Lemma.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Vasco Brattka
    • 1
    • 2
  • Guido Gherardi
    • 3
  • Rupert Hölzl
    • 2
  • Arno Pauly
    • 4
  1. 1.Deptartment of Mathematics and Applied MathematicsUniversity of Cape TownCape TownSouth Africa
  2. 2.Faculty of Computer ScienceUniversität der Bundeswehr MünchenNeubibergGermany
  3. 3.Dipartimento di Filosofia e ComunicazioneUniversità di BolognaBolognaItaly
  4. 4.Départment d’InformatiqueUniversité libre de BruxellesBrusselsBelgium

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