### Toward classification theory of good $\lambda$ frames and abstract elementary classes

by Shelah. [Sh:705]

Our main aim is to investigate a good lambda-frame
s which is as in the end of [600], i.e. s is n-successful for
every n (i.e. we can
define a good lambda^{+n}-frame s^{+n} such that
s^{+0} = s, s^{+(n+1)} =
(s^{+n})^+). We would like to prove then K^s has
model in every cardinal > lambda, and it is categorical in
one of them iff it is categorical in every one of
them. For this we shall show that K_{s^{+n}} 's are similar
to superstable elementary classse with prime existence. (Actually
also K^s_{>= lambda^{+ omega}}, but the full
proof are delayed).

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