On the Weihrauch Degree of the Additive Ramsey Theorem over the Rationals - Pradic, Cécilia; Soldà, Giovanni (Revolutions and Revelations in Computability, 2022)
We characterize the strength, in terms of Weihrauch degrees, of certain problems related to Ramsey-like theorems concerning colourings of the rationals. The theorems we are chiefly interested in assert the existence of almost-homogeneous sets for colourings of pairs of rationals satisfying properties determined by some additional algebraic structure on the set of colours. In the context of reverse mathematics, most of the principles we study are equivalent to Σ20 $$\varSigma ^0_2$$ -induction over RCA0 $$RCA_0$$ . The associated problems in the Weihrauch lattice are related to TCN∗ $$TC_{\mathbb {N}}^*$$ , (LPO′)∗ $$(LPO')^*$$ or their product, depending on their precise formalizations.