Metric abstract elementary classes with perturbations

Volume 217 / 2012

Åsa Hirvonen, Tapani Hyttinen Fundamenta Mathematicae 217 (2012), 123-170 MSC: Primary 03C52; Secondary 03C45. DOI: 10.4064/fm217-2-2

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.

Authors

  • Åsa HirvonenDepartment of Mathematics and Statistics
    University of Helsinki
    P.O. Box 68
    00014 University of Helsinki, Finland
    e-mail
  • Tapani HyttinenDepartment of Mathematics and Statistics
    University of Helsinki
    P.O. Box 68
    00014 University of Helsinki, Finland
    e-mail

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