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.
Matou s ek, Bounded VC-dimension implies a fractional Helly theorem, Discrete & Computational Geometry 31 (2004), no
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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.