Journal of Symbolic Logic 86 (1):316-351 (2021)

We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm {ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight different multivalued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility. In particular one of our functions turns out to be strictly stronger than any previously studied multivalued functions arising from statements around $\mathrm {ATR}_0$.
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DOI 10.1017/jsl.2021.10
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References found in this work BETA

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Closed Choice and a Uniform Low Basis Theorem.Vasco Brattka, Matthew de Brecht & Arno Pauly - 2012 - Annals of Pure and Applied Logic 163 (8):986-1008.
Effective Borel Measurability and Reducibility of Functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.
Completion of Choice.Vasco Brattka & Guido Gherardi - 2021 - Annals of Pure and Applied Logic 172 (3):102914.
Embeddings Between Well-Orderings: Computability-Theoretic Reductions.Jun Le Goh - 2020 - Annals of Pure and Applied Logic 171 (6):102789.

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