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arXiv · 2308.13942

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

John T. Baldwin·M. C. Laskowski·Saharon Shelah
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Abstract

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.

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John T. Baldwin, M. C. Laskowski, Saharon Shelah. 2023-08-26. When does $\aleph_1$-categoricity imply $\omega$-stability?. https://doi.org/10.2140/mt.2024.3.801

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