# Sh:734

• Shelah, S. Categoricity and solvability of A.E.C., quite highly. In Classification Theory for Abstract Elementary Classes. Preprint. arXiv: 0808.3023
Ch. IV of [Sh:h]
• Abstract:
We investigate in ZFC what can be the family of large enough cardinals \mu in which an a.e.c. \mathfrak{K} is categorical or even just solvable. We show that for not few cardinals \lambda < \mu there is a superlimit model in \mathfrak{K}_\lambda. Moreover, our main result is that we can find a good \lambda-frame \mathfrak{s} categorical in \lambda such that \mathfrak{K}_\mathfrak{s} \subseteq \mathfrak{K}_\lambda. We then show how to use 705 to get categoricity in every large enough cardinality if \mathfrak{K} has cases of \mu-amalgamation for enough \mu and 2^\mu < 2^{\mu^{+1}} < \ldots < 2^{\mu^{+n}} \ldots for enough \mu.
@inbook{Sh:734,
}