Baldwin's categoricity conjecture for atomic classes

Let TT be a countable first-order theory and let KTK_T be its class of atomic models. Baldwin's conjecture. If KTK_T is categorical in 1\beth_1, then KTK_T is 0\beth_0-stable, equivalently absolutely categorical. This asks whether categoricity in the first uncountable cardinal forces the strongest stability behavior for the atomic class; the source presents it as an unresolved question.

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Primary source

Saharon Shelah, “A.E.C. with not too many models”, arXiv:1302.4841 (2013).

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