Department of Mathematics
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Abstract Elementary Classes (aecs) were introduced by Shelah and developed further by Grossberg and others to allow the extension of some important techniques and ideas from classical first order model theory to non-classical settings (infinitary logics, extended quantifiers, etc). I will give a brief overview of the general context of clasical model theory, and present the definition of an abstract elementary class, relating the parts of the definition to the necessary tools of the classical theory.
Then I will discuss applications and examples from the model theory of modules, from joint work with Marcos-Mazari Armida, a recent PhD at Carnegie Mellon and a student of Grossberg.

References:

1. Mazari-Armida, Marcos, Algebraic description of limit models in classes of abelian groups, arXiv1810.02203
2. Thoomas G. Kucera, Mazari-Armida, Marcos, On universal modules with pure embeddings, arXiv1903.00414