Submission date: 26 July 2023

Abstract:

We consider finitary approximations of the (embedding) Ramsey property. Using a class of homogeneous reducts of random ordered hypergraphs, we prove that these properties form a strict hierarchy. We also show that every class of finite structures in which every structure of size at most 2 is a "Ramsey object" essentially consists of ordered structures, generalising a known result for countable Ramsey classes.

Mathematics Subject Classification: 05C55, 03C52

Keywords and phrases:

Full text arXiv 2307.14468: pdf, ps.