### Categoricity for abstract classes with amalgamation

by Shelah. [Sh:394]

Annals Pure and Applied Logic, 1999

Let K be an abstract elementary class with
amalgamation, and Lowenheim Skolem number LS (K) . We prove
that for a suitable Hanf number chi_0 if chi_0 < lambda_0 <=
lambda_1, and K is categorical in lambda^+_1 then it
is categorical in lambda_0 .

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