The Strong Small Index Property for Free Homogeneous Structures

2017/03/30 by Gianluca Paolini, Saharon Shelah, Paolini, Gianluca +1 · 2 citations
Mathematics · #03C15 #20B27 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1703.10517

openalex publication_date 2017/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that in algebraically locally finite countable homogeneous structures with a free stationary independence relation the small index property implies the strong small index property. We use this and the main result of [15] to deduce that countable free homogeneous structures in a locally finite relational language have the strong small index property. We also exhibit new continuum sized classes of ℵ₀-categorical structures with the strong small index property whose automorphism groups are pairwise non-isomorphic.

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