Parallel and Serial Jumps of Weak Weak König’s Lemma

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

Abstract

We study the principle of positive choice in the Weihrauch degrees. In particular, we study its behaviour under composition and jumps, and answer three questions asked by Brattka, Gherardi and Hölzl.

References

  1. 1.
    Bienvenu, L., Greenberg, N., Monin, B.: Continuous higher randomness. http://homepages.mcs.vuw.ac.nz/~greenberg/Papers
  2. 2.
    Brattka, V., Gherardi, G.: Weihrauch degrees, omniscience principles and weak computability. J. Symbolic Logic 76(1), 143–176 (2011)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Brattka, V., Gherardi, G., Hölzl, R.: Probabilistic computability and choice. Inf. Comput. 242, 249–286 (2015)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Brattka, V., Gherardi, G., Marcone, A.: The Bolzano-Weierstrass theorem is the jump of weak König’s lemma. Ann. Pure Appl. Logic 163, 623–655 (2012)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Brattka, V., Hendtlass, M., Kreuzer, A.P.: On the uniform computational content of computability theory. http://arxiv.org/pdf/1501.00433v3.pdf
  6. 6.
    Brattka, V., Pauly, A.: On the algebraic structure of Weihrauch degrees. http://arxiv.org/pdf/1604.08348v1.pdf
  7. 7.
    Brattka, V., Pauly, A.: Computation with advice. In: Zheng, X., Zhong, N. (eds.) CCA 2010, Proceedings of the Seventh International Conference on Computability and Complexity in Analysis, Electronic Proceedings in Theoretical Computer Science, pp. 41–55 (2010)Google Scholar
  8. 8.
    Downey, R.G., Hirschfeldt, D.R.: Algorithmic Randomness and Complexity. Theory and Applications of Computability. Springer, Heidelberg (2010)CrossRefMATHGoogle Scholar
  9. 9.
    Nies, A.: Computability and Randomness. Oxford Logic Guides. Oxford University Press, Oxford (2009)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LIRMM, CNRS & Université de MontpellierMontpellier Cedex 5France
  2. 2.Department of MathematicsUniversity of Wisconsin–MadisonMadisonUSA

Personalised recommendations