Exact saturation in simple and NIP theories

被引：5

作者：

Kaplan, Itay ^{[1
]}

Shelah, Saharon ^{[1
,2
]}

Simon, Pierre ^{[3
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus, IL-91904 Jerusalem, Israel

[2] Rutgers State Univ, Dept Math, Hill Ctr Busch Campus,110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

[3] Univ Claude Bernard Lyon 1, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

来源：

JOURNAL OF MATHEMATICAL LOGIC | 2017年 / 17卷 / 01期

基金：

以色列科学基金会; 欧洲研究理事会;

关键词：

Saturated models; classification theory; NIP theories; distal theories; simple theories;

D O I：

10.1142/S0219061317500015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A theory T is said to have exact saturation at a singular cardinal k if it has a k-saturated model which is not k(+) -saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.

引用

页数：18

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