On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension

被引：6

作者：

Guingona, Vincent ^{[1
]}

Hill, Cameron Donnay ^{[2
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[2] Wesleyan Univ, Dept Math & Comp Sci, Middletown, CT 06459 USA

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2015年 / 166卷 / 04期

关键词：

op-dimension; op-rank; dp-rank; 2-rank; o-minimal; NIP THEORIES;

D O I：

10.1016/j.apal.2014.11.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multi-order property, generalizing the order property, and use this to create op-rank, which generalizes 2-rank. From this we build op-dimension. We show that op-dimension bounds dp-rank, that op-dimension is sub-additive, and op-dimension generalizes o-minimal dimension in o-minimal theories. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：502 / 525

页数：24

共 17 条

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