关于Erdos-Moser定理的研究

本文主要研究Erdos-Moser定理。在简单介绍了反推数学的一些基础知识后，首先研究了Erdos-Moser定理的证明论强度：存在一个可计算的二元二染色函数使得任何无穷∑20集合都不是该函数的传递集，同时存在一个可计算的二元二染色函数使得每一个该函数的无穷传递集都是超免疫的。其次，我们进一步考虑了稳定性Erdos—Moser定理，证明了在二阶算术子系统RCA0下稳定性Erdos-Moser定理是不可证的并且对每一个可计算的稳定性二色二阶函数，我们构造了一个Ф’可计算的无穷传递集。

Some Results on Erdos-Moser Theorem

In this paper, we get some results on Erd6s-Moser theorem. After briefly intro- ducing some basic knowledge about reverse mathematics, we first investigate the strength of ErdOs-Moser theorem. There is a computable function f ： [ω] 2 → 2 such that no infinite Eo set is transitive for f. There is a computable function f ： [ω]2→ 2 such that every infinite transitive set for f is hyperimmune. Then we study the strength of stable Erdos-Moser theo- rem. We show that RCAo does not imply stable Erdos-Moser theorem and we also prove that t there exists a Ф -computable mflnite transitive set S for each given stable computable function f ： [ω] 2→ 2 by direct construction.