关于独立阶数

摘要：

本文研究了Shelah在其著作中提出的一个模型论不变量$κ_{srd}^m(T)$，证明了$κ_{srd}^m(T)$是次可加的.当$κ_{srd}^m(T)$是无限的，这给出了等式$κ^m_{srd}(T)=κ^1_{srd}(T)$，回答了Shelah的一个问题。我们用同样的证明方法分析了另一个不变量$κ^m_{ird}(T)$，证明了它也是次可加的，改进了书中的一个结果。

英文摘要：

We investigate a model theoretic invariant $κ_{srd}^m(T)$, which was introduced by Shelah in his famous book, and prove that $κ_{srd}^m(T)$ is sub-additive. When $κ_{srd}^m(T)$ is infinite, this gives the equality $κ^m_{srd}(T)=κ^1_{srd}(T)$, answering a question by Shelah. We apply the same proof method to analyze another invariant $κ^m_{ird}(T)$, and show that it is also sub-additive, improving a result in the book.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。