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# $$\mu$$-Abstract Elementary Classes and other generalizations

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### Abstract

We introduce $$\mu$$-Abstract Elementary Classes ($$\mu$$-AECs) as a broad framework for model theory that includes complete boolean algebras and Dirichlet series, 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: not least, the preliminary classification-theoretic results for {\mu}-AECs transfer directly to accessible categories with monomorphisms.

### Author and article information

###### Journal
2015-09-24
2016-02-11
1509.07377 10.1016/j.jpaa.2016.02.002

03C48 (Primary), 03C45, 18C35, 03C52, 03C55, 03C75, 03E55 (Secondary)
Journal of Pure and Applied Algebra 220 (2016), no. 9, 3048-3066
26 pp
math.LO math.CT

General mathematics, Logic & Foundation