Conservation strength of the infinite pigeonhole principle for trees

Abstract

Let TT1 be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let RT 2 2 and WKL0 denote respectively the principles of Ramsey’s theorem for pairs and the weak König lemma. It is proved that TT1 + RT 2 2 + WKL0 is Π 3 0 -conservative over the base system RCA0. Thus over RCA0, TT1 and Ramsey’s theorem for pairs prove the same Π 3 0 -sentences.