Abstract elementary class

In model theory, a discipline within mathematical logic, an abstract elementary class, or AEC for short, is a class of models with a partial order similar to the relation of an elementary substructure of an elementary class in first-order model theory. They were introduced by Saharon Shelah.

${\displaystyle \langle K,\prec _{K}\rangle }$, for ${\displaystyle K}$ a class of structures in some language ${\displaystyle L=L(K)}$, is an AEC if it has the following properties:

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