Infinitary Logics and Abstract Elementary Classes

We prove that every abstract elementary class (a.e.c.) with LST number \kappa and vocabulary \tau of cardinality \leq \kappa can be axiomatized in the logic {\mathbb L}_{\beth_2(\kappa)^{+++},\kappa^+}(\tau). In this logic an a.e.c. is therefore an EC class rather than merely a PC class. This constitutes a major improvement on the... Show more