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Categoricity from one successor cardinal in Tame Abstract Elementary Classes

Rami Grossberg, Monica VanDieren

Published 2005-09-30Version 1

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 \chi-tame. If K is categorical in some \lambda^+ >LS(K) then it is categorical in all \mu\geq (\lambda+\chi)^+. 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 \mu\geq LS(K).

Comments: 20 pages
Categories: math.LO
Subjects: 03C45, 03C52, 03C75
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