English

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 0\aleph_0-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}
}