Abstract elementary classes stable in N0

被引：7

作者：

Shelah, Saharon ^{[1
,2
]}

Vasey, Sebastien ^{[3
,4
]}

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] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

[4] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2018年 / 169卷 / 07期

基金：

美国国家科学基金会; 以色列科学基金会; 欧洲研究理事会;

关键词：

Abstract elementary classes; N-0-Stability; Good frames; Superlimit; Locality; QUASIMINIMAL STRUCTURES; CLASSIFICATION-THEORY; UNCOUNTABLE MODELS; SATURATED MODELS; CATEGORICITY; SUPERSTABILITY; INDEPENDENCE; SUCCESSOR; STABILITY; SYMMETRY;

D O I：

10.1016/j.apal.2018.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study abstract elementary classes (AECs) that, in N-0, have amalgamation, joint embedding, no maximal models and are stable (in terms of the number of orbital types). Assuming a locality property for types, we prove that such classes exhibit superstable-like behavior at N-0. More precisely, there is a superlimit model of cardinality 110 and the class generated by this superlimit has a type-full good N-0-frame (a local notion of nonforking independence) and a superlimit model of cardinality N-1. We also give a supersimplicity condition under which the locality hypothesis follows from the rest. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：565 / 587

页数：23

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