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Ramsey expansions of metrically homogeneous graphs

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By Andrés Ahumada Aranda, David B. Bradley-Williams, Czech Academy, Miltiadis Karamanlis
| tu-dresden.de
We investigate Ramsey expansions, the coherent extension property for partial isometries (EPPA), and the existence of a stationary independence relation for all classes of metrically homogeneous graphs from Cherlin’s catalogue. 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.
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