Micheal Pawliuk

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We prove that certain classes of metrically homogeneous graphs omitting triangles of odd short perimeter as well as triangles of long perimeter have the extension property for partial automorphisms and we describe their Ramsey expansions. This is extended variant of an extended abstract accepted to Eurocomb 2017 which contains proofs of the main statements.
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(More)
We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics. We determine precisely which of these automorphism groups are amenable (in their natural topologies). For those which are amenable, we determine whether they are uniquely ergodic, leaving(More)
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