On the strength of Ramsey's theorem for trees

Abstract Let TT 1 denote the principle that every finite coloring of the full binary tree has a homogeneous isomorphic subtree, i.e. one that is monochromatic. We show that over the system RCA 0 , the inductive strength of TT 1 is weaker than Σ 2 0 -induction. This follows from the main theorem that over the same system, TT 1 is Π 1 1 -conservative over Σ 2 0 -bounding plus the principle of the totality of the Ackermann function.