We continue the study of finitary abstract elementary classes beyond ℵ₀-stability. We suggest a possible notion of superstability for simple finitary AECs, and derive from this notion several good properties for independence. We also study constructible models and the behaviour of Galois types and weak Lascar strong types in this context. We show that superstability is implied by a-categoricity in a suitable cardinal. As an application we prove the following theorem: Assume that is a simple, tame, finitary AEC, a-categorical in some cardinal κ above the Hanf number such that cf(κ) > ω. Then is a-categorical in each cardinal above the Hanf number.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-3-3,
author = {Tapani Hyttinen and Meeri Kes\"al\"a},
title = {Superstability in simple finitary AECs},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {221-268},
zbl = {1125.03027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-3-3}
}
Tapani Hyttinen; Meeri Kesälä. Superstability in simple finitary AECs. Fundamenta Mathematicae, Tome 193 (2007) pp. 221-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-3-3/