A.E.C. with not too many models

by Shelah. [Sh:893]
Logic Without Borders, 2015
Consider an a.e.c. K and the class of {bold C}_{aleph_0} cardinals of cofinality aleph_0 . A nicely stated consequence of this work is for some closed unbounded class C of cardinals we have (a) quad dot I(lambda, K) >= lambda for lambda in C cap {bold C_{aleph_0}} or (b) quad if M in K_lambda and lambda in {bold C}_{aleph_0}, then M has le_K-extension (so in K) of arbitrarily large cardinals.

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