$\mu$-abstract elementary classes and other generalizations

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Authors

BONEY William Nelson GROSSBERG R. LIEBERMAN Michael ROSICKÝ Jiří VASEY S.

Year of publication 2016
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1016/j.jpaa.2016.02.002
Field General mathematics
Keywords abstract elementary class; accessible category
Description 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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