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Relational quotients

100%

Sokić M.

Fundamenta Mathematicae

2013

tom 221

nr 3

189-220

Let 𝒦 be a class of finite relational structures. We define ℰ𝒦 to be the class of finite relational structures A such that A/E ∈ 𝒦, where E is an equivalence relation defined on the structure A. Adding arbitrary linear orderings to structures from ℰ𝒦, we get the class 𝒪ℰ𝒦. If we add linear orderings to structures from ℰ𝒦 such that each E-equivalence class is an interval then we get the class 𝒞ℰ[𝒦*]. We provide a list of Fraïssé classes among ℰ𝒦, 𝒪ℰ𝒦 and 𝒞ℰ[𝒦*]. In addition, we classify 𝒪ℰ𝒦 and 𝒞ℰ[𝒦*] according to the Ramsey property. We also conduct the same analysis after adding additional structure to each equivalence class. As an application, we give a topological interpretation using the technique introduced in Kechris, Pestov and Todorčević. In particular, we extend the lists of known extremely amenable groups and universal minimal flows.

Dynamical properties of the automorphism groups of the random poset and random distributive lattice

63%

Kechris A., Sokić M.

Fundamenta Mathematicae

2012

tom 218

nr 1

69-94

A method is developed for proving non-amenability of certain automorphism groups of countable structures and is used to show that the automorphism groups of the random poset and random distributive lattice are not amenable. The universal minimal flow of the automorphism group of the random distributive lattice is computed as a canonical space of linear orderings but it is also shown that the class of finite distributive lattices does not admit hereditary order expansions with the Amalgamation Property.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Sokić M.

1 Kechris A.

1 2013

1 2012

Wyniki wyszukiwania

Relational quotients

Dynamical properties of the automorphism groups of the random poset and random distributive lattice