$\mu$-Abstract Elementary Classes and other generalizations

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 μ-AECs transfer directly to accessible categories with monomorphisms.

26 pp

References in corpus (4)

• Chains of saturated models in AECs
• Around the set-theoretical consistency of d-tameness of Metric Abstract Elementary Classes
• Accessible images revisited
• Categoricity and infinitary logics

Cited by in corpus (6)

• Forking independence from the categorical point of view
• Universal abstract elementary classes and locally multipresentable categories
• Internal sizes in $\mu$-abstract elementary classes
• Formal Model Theory & Higher Topology
• Cofinality quantifiers in Abstract Elementary Classes and beyond
• Accessible categories, set theory, and model theory: an invitation