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.
The research of the second author was supported by John Templeton Foundation grant 15619: ‘Mind, Mechanism and Mathematics: Turing Centenary Research Project’.
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Notes
- 1.
Our definition is not exactly the same as the definition of \(\mathrm {C}_{\omega }\) in Brattka, Gherardi and Hölzl [3], but it is easily seen to be strongly Weihrauch-equivalent to it.
- 2.
They do not explicitly state the strong Weihrauch equivalence, but it follows directly from their proof.
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Bienvenu, L., Kuyper, R. (2017). Parallel and Serial Jumps of Weak Weak König’s Lemma. In: Day, A., Fellows, M., Greenberg, N., Khoussainov, B., Melnikov, A., Rosamond, F. (eds) Computability and Complexity. Lecture Notes in Computer Science(), vol 10010. Springer, Cham. https://doi.org/10.1007/978-3-319-50062-1_15
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