# 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…

## 27 Citations

### Semigroup-valued metric spaces

- Mathematics
- 2019

The structural Ramsey theory is a field on the boundary of combinatorics and model theory with deep connections to topological dynamics. Most of the known Ramsey classes in finite binary symmetric…

### Semigroup-valued metric spaces

- Mathematics
- 2018

The structural Ramsey theory is a field on the boundary of combinatorics and model theory with deep connections to topological dynamics. Most of the known Ramsey classes in finite binary symmetric…

### Combinatorial Properties of Metrically Homogeneous Graphs

- MathematicsArXiv
- 2018

This thesis finds Ramsey expansions of the primitive 3-constrained classes from Cherlin's catalogue of metrically homogeneous graphs, which implies the extension property for partial automorphisms (EPPA), another combinatorial property of classes of finite structures.

### Ramsey Classes with Closure Operations (Selected Combinatorial Applications)

- MathematicsArXiv
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The Ramsey property of classes of ordered structures with closures and given local properties is state, providing the ultimate generalisation of Structural Ramsey Theorem and several applications are shown.

### Combinatorial Properties of Metrically Homogeneous Graphs

- Mathematics
- 2018

This thesis finds Ramsey expansions of the primitive 3-constrained classes from Cherlin’s catalogue of metrically homogeneous graphs, which implies the extension property for partial automorphisms (EPPA), another combinatorial property of classes of finite structures.

### All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)

- Mathematics
- 2019

A general theorem showing the extension property for partial automorphisms (EPPA) for classes of structures containing relations and unary functions, optionally equipped with a permutation group of the language is proved.

### BACHELOR THESIS Matěj Konečný Combinatorial Properties of Metrically Homogeneous Graphs

- Mathematics
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Ramsey theory looks for regularities in large objects. Model theory studies algebraic structures as models of theories. The structural Ramsey theory combines these two fields and is concerned with…

### Ramsey Classes with Closure Operations

- Mathematics
- 2017

We state the Ramsey property of classes of ordered structures with closures and given local properties. This generalises many old and new results: the Nešetřil-Rödl Theorem, the authors Ramsey lift…

### EPPA for two-graphs and antipodal metric spaces

- MathematicsArXiv
- 2018

We prove that the class of two-graphs has the extension property for partial automorphisms (EPPA, or Hrushovski property), thereby answering a question of Macpherson. In other words, we show that the…

### All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)

- MathematicsArXiv
- 2019

A general theorem showing the extension property for partial automorphisms (EPPA) for classes of structures containing relations and unary functions, optionally equipped with a permutation group of the language.

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