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Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic

Volume 234 / 2016

Karim Khanaki Fundamenta Mathematicae 234 (2016), 253-286 MSC: Primary 03B48, 03C45, 28C10, 43A07. DOI: 10.4064/fm208-1-2016 Published online: 2 May 2016

Abstract

This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup such as amenability and the fixed point on compacta property. Second, we define types and develop local stability in the framework of integral logic. For a stable formula $\phi $, we prove definability of all complete $\phi $-types over models and deduce from this the fundamental theorem of stability. Third, we study an important property in measure theory, Talagrand’s stability. We point out the connection between Talagrand’s stability and dependence property (NIP), and prove a measure-theoretic version of definability of types for NIP formulas.

Authors

  • Karim KhanakiFaculty of Fundamental Sciences
    Arak University of Technology
    38135-1177, Arak, Iran
    and
    School of Mathematics
    Institute for Research in Fundamental Sciences
    19395-5746, Tehran, Iran
    e-mail
    e-mail

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