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# Categoricity in Abstract Elementary Classes: Going up Inductive Step Sh600 -part 1 and 2

@inproceedings{ShelahCategoricityIA, title={Categoricity in Abstract Elementary Classes: Going up Inductive Step Sh600 -part 1 and 2}, author={Saharon Shelah} }

We deal with beginning stability theory for " reasonable " non-elementary classes without any remnants of compactness like dealing with models above Hanf number or by the class being definable by L ω 1 ,ω. We introduce and investigate good λ-frame, show that they can be found under reasonable assumptions and prove we can advance from λ to λ + when non-structure fail. That is, assume 2 λ +n < 2 λ +n+1 for n < ω. So if an a.e.c. is cateogorical in λ, λ + and has intermediate number of models in… CONTINUE READING