Categoricity from one successor cardinal in Tame Abstract Elementary Classes
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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\geq (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\geq LS(K).
20 pages
20 pages