Metric abstract elementary classes with perturbations

Åsa Hirvonen, and Tapani Hyttinen. "Metric abstract elementary classes with perturbations." Fundamenta Mathematicae 217.2 (2012): 123-170. <http://eudml.org/doc/282626>.

@article{ÅsaHirvonen2012,
abstract = {We define an abstract setting suitable for investigating perturbations of metric structures generalizing the notion of a metric abstract elementary class. We show how perturbation of Hilbert spaces with an automorphism and atomic Nakano spaces with bounded exponent fit into this framework, where the perturbations are built into the definition of the class being investigated. Further, assuming homogeneity and some other properties true in the example classes, we develop a notion of independence for this setting and show that it satisfies the usual independence axioms. Finally we define an isolation notion. Although it remains open whether this isolation gives any reasonable form of primeness, we prove that dominance works.},
author = {Åsa Hirvonen, Tapani Hyttinen},
journal = {Fundamenta Mathematicae},
keywords = {metric structures; perturbation; metric abstract elementary classes},
language = {eng},
number = {2},
pages = {123-170},
title = {Metric abstract elementary classes with perturbations},
url = {http://eudml.org/doc/282626},
volume = {217},
year = {2012},
}

TY - JOUR
AU - Åsa Hirvonen
AU - Tapani Hyttinen
TI - Metric abstract elementary classes with perturbations
JO - Fundamenta Mathematicae
PY - 2012
VL - 217
IS - 2
SP - 123
EP - 170
AB - We define an abstract setting suitable for investigating perturbations of metric structures generalizing the notion of a metric abstract elementary class. We show how perturbation of Hilbert spaces with an automorphism and atomic Nakano spaces with bounded exponent fit into this framework, where the perturbations are built into the definition of the class being investigated. Further, assuming homogeneity and some other properties true in the example classes, we develop a notion of independence for this setting and show that it satisfies the usual independence axioms. Finally we define an isolation notion. Although it remains open whether this isolation gives any reasonable form of primeness, we prove that dominance works.
LA - eng
KW - metric structures; perturbation; metric abstract elementary classes
UR - http://eudml.org/doc/282626
ER -