• Corpus ID: 24996994

Ramsey expansions of metrically homogeneous graphs

@article{Aranda2017RamseyEO,
  title={Ramsey expansions of metrically homogeneous graphs},
  author={Andr{\'e}s Aranda and David Bradley-Williams and Jan Hubicka and Miltiadis Karamanlis and Michael Kompatscher and Matej Konecn{\'y} and Micheal Pawliuk},
  journal={ArXiv},
  year={2017},
  volume={abs/1707.02612}
}
We discuss the Ramsey property, the existence of a stationary independence relation and the coherent extension property for partial isometries (coherent EPPA) for all classes of metrically homogeneous graphs from Cherlin's catalogue, which is conjectured to include all such structures. We show that, with the exception of tree-like graphs, all metric spaces in the catalogue have precompact Ramsey expansions (or lifts) with the expansion property. With two exceptions we can also characterise the… 

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