The following are examples of abstract elementary classes:[REF] .
If \phi is a sentence in the infinitary logic L_{\omega_1, \omega}, and \mathcal{F} is a countable fragment containing \phi, then \langle \operatorname{Mod}(T), \prec_{\mathcal{F}} \rangle is an AEC with Löwenheim-Skolem number \aleph_0.