Categoricity from one successor cardinal in Tame Abstract Elementary Classes
Rami Grossberg, Monica VanDieren
Abstract
Let K be an abstract elementary classes which has arbitrarily large models and satisfies the amalgamation and joint embedding properties. Theorem 1. Suppose K is χ-tame. If K is categorical in some λ+ >LS(K) then it is categorical in all μ≥ (λ+χ)+. Theorem 2. If K is LS(K)-tame and is categorical both in LS(K) and in LS(K)+ then K is categorical in all μ≥ LS(K).
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