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.
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