# 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]}
}