How strong is Ramsey's theorem if infinity can be weak?

Leszek Aleksander Kołodziejczyk, Katarzyna W. Kowalik, Keita Yokoyama

We study the first-order consequences of Ramsey's Theorem for $k$-colourings of $n$-tuples, for fixed $n,k\ge 2$, over the relatively weak second-order arithmetic theory $\mathrm…