On the strength of Ramsey's theorem for trees

Abstract

Let TT1 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 RCA0, the inductive strength of TT1 is weaker than Σ20-induction. This follows from the main theorem that over the same system, TT1 is Π11-conservative over Σ20-bounding plus the principle of the totality of the Ackermann function.