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.
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页码：3048 / 3066
页数：19
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