We show that the class of finite rooted binary plane trees is a Ramsey class (with respect to topological embeddings that map leaves to leaves). That is, for all such trees P,H and every natural number k there exists a tree T such that for every k-coloring of the (topological) copies of P in T there exists a (topological) copy H' of H in T such that all copies of P in H' have the same color. When the trees are represented by the so-called rooted triple relation, the result gives rise to a Ramsey class of relational structures with respect to induced substructures.
Preparation Semilinear order relations Abstract chain sets General betweenness relations Abstract direction sets Applications and commentary References. 1. Introduction 2. Preliminaries 3. Examples and growth rates 4. Subgroups 5. Miscellaneous topics.