On the number of independent orders

被引：1
|
作者：
Takeuchi, Kota [1 ]
Tsuboi, Akito [1 ]
机构：
[1] Univ Tsukuba, Inst Math, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058571, Japan
来源：
ANNALS OF PURE AND APPLIED LOGIC | 2021年 / 172卷 / 02期
关键词：
Strict order property; NIP; Mutual indiscernibility; Sub-additivity;
D O I：
10.1016/j.apal.2020.102886
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the model-theoretic invariant kappa(m)(srd)(T), which was introduced by Shelah, and prove that kappa(m)(srd)(T) is sub-additive. An infinite value of kappa(m)(srd)(T) leads to the equality kappa(m)(srd)(T) = kappa(1)(srd)(T). We apply the same proof method to analyze the other invariant kappa(m)(ird)(T) and show that it is also sub-additive, achieving an improvement of Shelah's result. (C) 2020 Elsevier B.V. All rights reserved.
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页数：8
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