# Sh:705

- Shelah, S. (2009).
*Toward classification theory of good \lambda frames and abstract elementary classes*. In Classification Theory for Abstract Elementary Classes. arXiv: math/0404272

Ch. III of [Sh:h] -
Abstract:

Our main aim is to investigate a good \lambda-frame \mathfrak{s} which is as in the end of [600], i.e. \mathfrak{s} is n-successful for every n (i.e. we can define a good \lambda^{+n}-frame \mathfrak{s}^{+n} such that \mathfrak{s}^{+0} =\mathfrak{s},\mathfrak{s}^{+(n+1)} = (\mathfrak{s}^{+n})^+). We would like to prove then K^\mathfrak{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_{\mathfrak{s}^{+n}}’s are similar to superstable elementary classse with prime existence. (Actually also K^\mathfrak{s}_{\ge \lambda^{+ \omega}}, but the full proof are delayed). - Version 2013-06-01_10 (230p)

Bib entry

@inbook{Sh:705, author = {Shelah, Saharon}, title = {{Toward classification theory of good $\lambda$ frames and abstract elementary classes}}, booktitle = {{Classification Theory for Abstract Elementary Classes}}, year = {2009}, note = {\href{https://arxiv.org/abs/math/0404272}{arXiv: math/0404272} Ch. III of [Sh:h]}, arxiv_number = {math/0404272}, refers_to_entry = {Ch. III of [Sh:h]} }