Metric abstract elementary classes with perturbations

• Autorzy: Åsa Hirvonen , Tapani Hyttinen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03C52: Properties of classes of models
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 217
• Numer: 2
• Strony: 123-170

Daty

wydano

2012

Twórcy

autor

Åsa Hirvonen

• Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 University of Helsinki, Finland

autor

Tapani Hyttinen

• Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 University of Helsinki, Finland

Identyfikatory

DOI

10.4064/fm217-2-2