Let TT¹ be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let RT ²₂ and WKL₀ denote respectively the principles of Ramsey’s theorem for pairs and the weak König lemma. It is proved that TT¹ + RT ²₂ + WKL₀ is Π ⁰₃ -conservative over the base system RCA₀. Thus over RCA₀, TT¹ and Ramsey’s theorem for pairs prove the same Π ⁰₃ -sentences.

中文翻译：

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树木无限鸽巢原理的守恒强度

令 TT ¹为组合原理，说明无限满二叉树的每个有限着色都有一个齐次同构子树。令RT ² ₂和WKL ₀分别表示拉姆齐对定理和弱König 引理的原理。证明了TT ¹ + RT ² ₂ + WKL ₀相对于基本系统RCA ₀是Π ⁰ _{3 -}保守的。因此，通过 RCA ₀、TT ¹和拉姆齐成对定理证明了相同的 Π ⁰ ₃ -句子。