Categoricity from one successor cardinal in Tame Abstract Elementary Classes

Details Categoricity from one successor cardinal in Tame Abstract Elementary Classes Categoricity from one successor cardinal in Tame Abstract Elementary Classes

2005-09-30

arxiv.org/abs/math/0510004v1

Mathematics

Logic

20 pages

Scientific paper

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).

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