### Almost Galois $\omega$-Stable classes

by Baldwin and Larson and Shelah. [BlLrSh:1003]

Theorem. Suppose that an aleph_0-presentable Abstract
Elementary Class (AEC), mathbf {K}, has the joint embedding and
amalgamation properties in aleph_0 and <2^{aleph_1} models in
aleph_1 . If mathbf {K} has only countably many models in
aleph_1, then all are small. If, in addition, mathbf {K} is
almost Galois omega-stable then mathbf {K} is Galois
omega-stable.

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