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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References found in this work BETA
Effective Choice and Boundedness Principles in Computable Analysis.Vasco Brattka & Guido Gherardi - 2011 - Bulletin of Symbolic Logic 17 (1):73-117.
Embeddings Between Well-Orderings: Computability-Theoretic Reductions.Jun Le Goh - 2020 - Annals of Pure and Applied Logic 171 (6):102789.
The Bolzano–Weierstrass Theorem is the Jump of Weak Kőnig’s Lemma.Vasco Brattka, Guido Gherardi & Alberto Marcone - 2012 - Annals of Pure and Applied Logic 163 (6):623-655.
Effective Borel Measurability and Reducibility of Functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.
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Citations of this work BETA
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Finding Descending Sequences Through Ill-Founded Linear Orders.Jun le Goh, Arno Pauly & Manlio Valenti - 2021 - Journal of Symbolic Logic 86 (2):817-854.
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