The Strong Small Index Property for Free Homogeneous Structures
Logic
2018-10-05 v3
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 -categorical structures with the strong small index property whose automorphism groups are pairwise non-isomorphic.
Keywords
Cite
@article{arxiv.1703.10517,
title = {The Strong Small Index Property for Free Homogeneous Structures},
author = {Gianluca Paolini and Saharon Shelah},
journal= {arXiv preprint arXiv:1703.10517},
year = {2018}
}