If a theory is categorical in one nonzero arithmetic degree then it is categorical in all nonzero arithmetic degrees, and this is equivalent to uncountable categoricity.
Kaplan, A definable (p,q) -theorem for NIP theories, Advances in Mathematics 436 (2024), 109418
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Categoricity without Power
If a theory is categorical in one nonzero arithmetic degree then it is categorical in all nonzero arithmetic degrees, and this is equivalent to uncountable categoricity.