Submission date: 30 March 2017

Abstract:

We show that in countable homogeneous structures with canonical amalgamation and locally finite algebraicity the small index property implies the strong small index property. We use this and the main result of [12] to deduce that countable free homogeneous structures in a locally finite irreflexive relational language have the strong small index property. As an application, we exhibit new continuum sized classes of ℵ_0-categorical structures with the strong small index property whose automorphism groups are pairwise non-isomorphic.

Mathematics Subject Classification: 20B27, 03C15

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Full text arXiv 1703.10517: pdf, ps.