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- Title
THE OPEN AND CLOPEN RAMSEY THEOREMS IN THE WEIHRAUCH LATTICE.
- Authors
MARCONE, ALBERTO; VALENTI, MANLIO
- Abstract
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 (five corresponding to the open Ramsey theorem and three corresponding to the clopen Ramsey theorem) 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 $\mathrm {ATR}_0$.
- Subjects
REVERSE mathematics; RAMSEY theory; ARITHMETIC
- Publication
Journal of Symbolic Logic, 2021, Vol 86, Issue 1, p316
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2021.10