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The Strong Small Index Property for Free Homogeneous Structures

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arxiv 1703.10517 v3 pith:4XQ35HMW submitted 2017-03-30 math.LO

Gianluca Paolini , Saharon Shelah This is my paper · ORCID
classification math.LO
keywords indexpropertysmallstrongstructuresfreehomogeneouscountable
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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 $\aleph_0$-categorical structures with the strong small index property whose automorphism groups are pairwise non-isomorphic.

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  1. A guide to topological reconstruction on endomorphism monoids and polymorphism clones

    math.LO 2025-11 conditional novelty 7.0 of 10

    Automatic homeomorphicity lifts from automorphism groups to elementary-embedding monoids for all countable saturated structures, and a new ω-stable counterexample delimits the failure for endomorphism monoids.

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