Superstability in simple finitary AECs

Tapani Hyttinen, and Meeri Kesälä. "Superstability in simple finitary AECs." Fundamenta Mathematicae 195.3 (2007): 221-268. <http://eudml.org/doc/282970>.

@article{TapaniHyttinen2007,
abstract = {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.},
author = {Tapani Hyttinen, Meeri Kesälä},
journal = {Fundamenta Mathematicae},
keywords = {abstract elementary class; independence; superstability; primary model},
language = {eng},
number = {3},
pages = {221-268},
title = {Superstability in simple finitary AECs},
url = {http://eudml.org/doc/282970},
volume = {195},
year = {2007},
}

TY - JOUR
AU - Tapani Hyttinen
AU - Meeri Kesälä
TI - Superstability in simple finitary AECs
JO - Fundamenta Mathematicae
PY - 2007
VL - 195
IS - 3
SP - 221
EP - 268
AB - 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.
LA - eng
KW - abstract elementary class; independence; superstability; primary model
UR - http://eudml.org/doc/282970
ER -