All These Approximate Ramsey Properties
Combinatorics
2023-07-28 v1 Logic
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.
Cite
@article{arxiv.2307.14468,
title = {All These Approximate Ramsey Properties},
author = {Nadav Meir and Aris Papadopoulos},
journal= {arXiv preprint arXiv:2307.14468},
year = {2023}
}
Comments
15 pages. arXiv admin note: text overlap with arXiv:2212.08027