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

We study the first-order consequences of Ramsey's Theorem for k-colourings of n-tuples, for fixed n, k >= 2, over the relatively weak second-order arithmetic theory RCA(0)(*). Using the Chong-Mourad coding lemma, we show that in a model of RCA(0)(*) that does not satisfy Sigma(0)(1) induction, RTkn is equivalent to its relativization to any proper Sigma(0)(1) -definable cut, so its truth value remains unchanged in all extensions of the model with the same first-order universe.