Big Ramsey degrees of 3-uniform hypergraphs are finite

Martin Balko, David Chodounský, Jan Hubička, Matěj Konečný, Lluis Vena

Published 2020-08-01Version 1

Generalizing the passing number construction by Sauer, we give a short proof of the fact that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. Our proof is based on vector (or product) form of the Milliken's tree theorem and demonstrates a general method to carry existing results on structures in binary relational languages to higher arities.