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Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes
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]).Comment: 19 page