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.

中文翻译：

---

关于树的拉姆齐定理的强度

摘要 令TT 1 表示全二叉树的每个有限着色都有一个同构同构子树，即单色子树。我们表明，在系统 RCA 0 上，TT 1 的感应强度弱于 Σ 2 0 -induction。这遵循以下主要定理：在同一系统上，TT 1 是 Π 1 1 -在 Σ 2 0 -边界上的保守加上阿克曼函数的总体原理。