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

Karim Khanaki. "Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic." Fundamenta Mathematicae 234.3 (2016): 253-286. <http://eudml.org/doc/286523>.

@article{KarimKhanaki2016,
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 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.},
author = {Karim Khanaki},
journal = {Fundamenta Mathematicae},
keywords = {amenability; extreme amenability; integral logic; local stability; dependence property; continuous logic},
language = {eng},
number = {3},
pages = {253-286},
title = {Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic},
url = {http://eudml.org/doc/286523},
volume = {234},
year = {2016},
}

TY - JOUR
AU - Karim Khanaki
TI - Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic
JO - Fundamenta Mathematicae
PY - 2016
VL - 234
IS - 3
SP - 253
EP - 286
AB - 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.
LA - eng
KW - amenability; extreme amenability; integral logic; local stability; dependence property; continuous logic
UR - http://eudml.org/doc/286523
ER -