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arXiv:2308.13942 [math.LO]AbstractReferencesReviewsResources

When does $\aleph_1$-categoricity imply $ω$-stability?

John T. Baldwin, M. C. Laskowski, Saharon Shelah

Published 2023-08-26Version 1

For an $\aleph_1$-categorical atomic class, we clarify the space of types over the unique model of size $\aleph_1$. Using these results, we prove that if such a class has a model of size $\beth_1^+$ then it is $\omega$-stable.

Comments: 22 pages
Categories: math.LO
Subjects: 03C45
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