The strong small index property for free homogeneous structures
by Paolini and Shelah. [PaSh:1108]
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 [siniora]
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
aleph_0-categorical structures with the strong small index
property whose automorphism groups are pairwise non-isomorphic.
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