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  1. The open and clopen Ramsey theorems in the Weihrauch lattice.Alberto Marcone & Manlio Valenti - 2021 - Journal of Symbolic Logic 86 (1):316-351.
    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 (...)
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  • Searching for an analogue of atr0 in the Weihrauch lattice.Takayuki Kihara, Alberto Marcone & Arno Pauly - 2020 - Journal of Symbolic Logic 85 (3):1006-1043.
    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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  • The computational strength of matchings in countable graphs.Stephen Flood, Matthew Jura, Oscar Levin & Tyler Markkanen - 2022 - Annals of Pure and Applied Logic 173 (8):103133.
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