EXTERNALLY DEFINABLE SETS AND DEPENDENT PAIRS II

被引：41

作者：

Chernikov, Artem ^{[1
,2
]}

Simon, Pierre ^{[1
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

[2] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 07期

关键词：

NIP; UDTFS; externally definable sets; VC-dimension; elementary pairs; MINIMAL THEORIES; FORKING; NIP;

D O I：

10.1090/S0002-9947-2015-06210-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We continue investigating the structure of externally definable sets in NIP theories and preservation of NIP after expanding by new predicates. Most importantly: types over finite sets are uniformly definable; over a model, a family of non-forking instances of a formula (with parameters ranging over a type-definable set) can be covered with finitely many invariant types; we give some criteria for the boundedness of an expansion by a new predicate in a distal theory; naming an arbitrary small indiscernible sequence preserves NIP, while naming a large one doesn't; there are models of NIP theories over which all 1-types are definable, but not all n-types.

引用

页码：5217 / 5235

页数：19