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- Andrés Aranda, David Bradley-Williams, +5 authors Micheal Pawliuk
- Electronic Notes in Discrete Mathematics
- 2017

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.

- Andrés Aranda, David Bradley-Williams, +4 authors Micheal Pawliuk
- ArXiv
- 2017

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)

- Gareth Boxall, David Bradley-Williams, Charlotte Kestner, Alexandra Omar Aziz, Davide Penazzi
- Notre Dame Journal of Formal Logic
- 2013

We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev. Our main results are that this notion characterises linearity in the setting of geometric þ-rank 1 structures and that lovely pairs of weakly one-based geometric þ-rank 1 structures are weakly one-based with respect to þ-independence. We also study geometries… (More)

A partial order is called semilinear iff the upper bounds of each element are linearly ordered and any two elements have a common upper bound. There exists, up to isomorphism, a unique countable semilinear order which is dense, unbounded, binary branching, and without joins, which we denote by (S2;≤). We study the reducts of (S2;≤), that is, the relational… (More)

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