We investigate the model-theoretic invariant ${\kappa }_{srd}^m(T)$, which was introduced by Shelah, and prove that ${\kappa }_{srd}^m(T)$ is sub-additive. An infinite value of ${\kappa }_{srd}^m(T)$ leads to the equality ${\kappa }_{srd}^m(T)={\kappa }_{srd}^1(T)$. We apply the same proof method to analyze the other invariant ${\kappa }_{ird}^m(T)$ and show that it is also sub-additive, achieving an improvement of Shelah's result.

中文翻译：

---

关于独立订单的数量

我们研究模型理论的不变性 ${\kappa }_{s\mathrm{[R}d}^{米}（Ť）$，由谢拉（Shelah）介绍，并证明 ${\kappa }_{s\mathrm{[R}d}^{米}（Ť）$是次加性的。的无限值${\kappa }_{s\mathrm{[R}d}^{米}（Ť）$ 导致平等 ${\kappa }_{s\mathrm{[R}d}^{米}（Ť）={\kappa }_{s\mathrm{[R}d}^{\mathrm{1个}}（Ť）$。我们采用相同的证明方法来分析其他不变式${\kappa }_{\mathrm{一世}\mathrm{[R}d}^{米}（Ť）$ 并表明它也是次加性的，从而改善了Shelah的结果。