On the absoluteness of orbital $\omega$-stability

by Larson and Shelah. [LrSh:1073]

We show that orbital omega-stability is upwards absolute (but not downwards absolute) for aleph_0-presented Abstract Elementary Classes satisfying amalgamation and the joint embedding property (each for countable models). We also show that amalgamation does not imply upwards absoluteness of orbital omega-stability by itself. The corresponding question for the joint embedding property remains open.

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