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arXiv · 1703.10517

The Strong Small Index Property for Free Homogeneous Structures

Gianluca Paolini·Saharon Shelah
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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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Gianluca Paolini, Saharon Shelah. 2017-03-30. The Strong Small Index Property for Free Homogeneous Structures. https://arxiv.org/abs/1703.10517

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