$\mu$-Abstract Elementary Classes and other generalizations
Will Boney, Rami Grossberg, Michael Lieberman, Jiri Rosicky, Sebastien, Vasey

TL;DR
This paper introduces $0$-Abstract Elementary Classes ($0$-AECs), a broad framework in model theory that encompasses structures like boolean algebras and Dirichlet series, and explores their classification theory.
Contribution
It defines $0$-AECs, connects them to accessible categories with monomorphisms, and initiates their classification-theoretic analysis.
Findings
$0$-AECs include various mathematical structures.
Classification results for $0$-AECs transfer to accessible categories.
Preliminary classification theory for $0$-AECs is developed.
Abstract
We introduce -Abstract Elementary Classes (-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 -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.
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