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arXiv · 1509.07377

$\mu$-Abstract Elementary Classes and other generalizations

Will Boney·Rami Grossberg·Michael Lieberman·Jiri Rosicky·Sebastien Vasey
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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.

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Will Boney, Rami Grossberg, Michael Lieberman, Jiri Rosicky, Sebastien Vasey. 2015-09-24. $\mu$-Abstract Elementary Classes and other generalizations. https://doi.org/10.1016/j.jpaa.2016.02.002

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