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.

引用

页数：8