Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes

Details Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes

2005-09-16

arxiv.org/abs/math/0509387v2

Mathematics

Logic

19 pages

Scientific paper

Let K be an Abstract Elemenetary Class satisfying the amalgamation and the joint embedding property, let \mu be the Hanf number of K. Suppose K is tame. MAIN COROLLARY: (ZFC) If K is categorical in a successor cardinal bigger than \beth_{(2^\mu)^+} then K is categorical in all cardinals greater than \beth_{(2^\mu)^+}. This is an improvment of a Theorem of Makkai and Shelah ([Sh285] who used a strongly compact cardinal for the same conclusion) and Shelah's downward categoricity theorem for AECs with amalgamation (from [Sh394]).

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