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

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Let K be an Abstract Elemenetary Class satisfying the amalgamation and the joint embedding property, let μbe the Hanf number of K. Suppose K is tame. MAIN COROLLARY: (ZFC) If K is categorical in a successor cardinal bigger than \beth_{(2^μ)^+} then K is categorical in all cardinals greater than \beth_{(2^μ)^+}. 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]).
19 pages

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Logic, 03C35;03C45;03C75

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http://salesiana.dossiersoluciones.com/handle/123456789/94638

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509387
 http://arxiv.org/abs/math/0509387

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arXiv