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

• Autorzy: Karim Khanaki
• Języki publikacji: EN

Abstrakty

EN

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 ϕ, we prove definability of all complete ϕ-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.

Kategorie tematyczne

• 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 03B48: Probability and inductive logic
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 234
• Numer: 3
• Strony: 253-286

Daty

wydano

2016

Twórcy

autor

Karim Khanaki

• Faculty of Fundamental Sciences, Arak University of Technology, 38135-1177, Arak, Iran
• School of Mathematics, Institute for Research in Fundamental Sciences, 19395-5746, Tehran, Iran

Identyfikatory

DOI

10.4064/fm208-1-2016