$\mathsf{RT}_k^1$问题的广义低解
Generalized low solution of $\mathsf{RT}_k^1$ problem
摘要：
我们研究了任意$\mathsf{RT}_k^1$实例的“编码能力”。证明了每个$\mathsf{RT}_k^1$ -实例都存在非平凡广义低解.这与Patey提出的一个问题有些关系。我们还回答了刘提出的一个问题，即，证明了存在一个$\mathbf{0}'$ -可计算的$\mathsf{RT}_3^1$ -实例$I_3^1$，使得每个$\mathsf{RT}_2^1$ -实例都有一个非平凡解，该解不计算$I_3^1$的任何非平凡解.
英文摘要：
We study the "coding power" of an arbitrary $\mathsf{RT}_k^1$-instance. We prove that every $\mathsf{RT}_k^1$-instance admit non trivial generalized low solution. This is somewhat related to a problem proposed by Patey. We also answer a question proposed by Liu, i.e., we prove that there exists a $\mathbf{0}'$-computable $\mathsf{RT}_3^1$-instance, $I_3^1$, such that every $\mathsf{RT}_2^1$-instance admit a non trivial solution that does not compute any non trivial solution of $I_3^1$.
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