Subrecursive complexity of identifying the Ramsey structure of posets

Abstract

We show that finite ordinal sums of finite antichains are Ramsey objects in the category of finite posets and height-preserving embeddings. Our proof yields a primitive recursive algorithm for constructing the finite posets which contain the required homogeneities. We also find, in terms of the classical Ramsey numbers, best possible upper bounds for the heights of the posets in which the homogeneous structures can be found. © 2008 Springer-Verlag Berlin Heidelberg.