$\mu$-abstract elementary classes and other generalizations
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Pure and Applied Algebra |
| MU Faculty or unit | |
| 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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