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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