Journal of Symbolic Logic 85 (3):1006-1043 (2020)

Abstract
There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.
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DOI 10.1017/jsl.2020.12
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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.
Embeddings Between Well-Orderings: Computability-Theoretic Reductions.Jun Le Goh - 2020 - Annals of Pure and Applied Logic 171 (6):102789.

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