Low-like basis theorems for Ramsey's theorem for pairs in first-order arithmetic

Hiroyuki Ikari, Keita Yokoyama

We construct an ${\ll }^2$-solution (also known as a weakly low solution) to ${\mathrm{D}}^2$ within $\mathrm{B}{\Sigma }_3^0$ and prove the ${\ll }^2$-basis theorem for ${\mathrm{RT}}^2$ over…