μ-Abstract elementary classes and other generalizations

被引：16

作者：

Boney, Will ^{[1
]}

Grossberg, Rami ^{[2
]}

Lieberman, Michael ^{[3
]}

Rosicky, Jiri ^{[3
]}

Vasey, Sebastien ^{[2
]}

机构：

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

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

[3] Masaryk Univ, Fac Sci, Dept Math & Stat, CS-61137 Brno, Czech Republic

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2016年 / 220卷 / 09期

基金：

瑞士国家科学基金会; 美国国家科学基金会;

关键词：

CLASSIFICATION-THEORY; UNCOUNTABLE MODELS; CATEGORICITY; SUCCESSOR; NUMBER;

D O I：

10.1016/j.jpaa.2016.02.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce mu-Abstract Elementary Classes (mu-AECs) as a broad framework for model theory that includes complete boolean algebras and metric spaces, and begin to develop their classification theory. Moreover, we note that mu-AECs correspond precisely to accessible categories in which all morphisms are monomorphisms, and begin the process of reconciling these divergent perspectives: for example, the preliminary classification-theoretic results for mu-AECs transfer directly to accessible categories with monomorphisms. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：3048 / 3066

页数：19

共 44 条

[41] Superstability in Q-Abstract Elementary Clases
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BOLETIN DE MATEMATICAS, 2023, 30 (02): : 6 - 9
[42] Categoricity for abstract classes with amalgamation
Shelah, S
ANNALS OF PURE AND APPLIED LOGIC, 1999, 98 (1-3) : 261 - 294
[43] Categoricity of an abstract elementary class in two successive cardinals
Saharon Shelah
Israel Journal of Mathematics, 2001, 126 : 29 - 128
[44] Exact saturation in pseudo-elementary classes for simple and stable theories
Kaplan, Itay
Ramsey, Nicholas
Shelah, Saharon
JOURNAL OF MATHEMATICAL LOGIC, 2022,

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