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Big Ramsey degrees of 3-uniform hypergraphs are finite (2008.00268v3)
Published 1 Aug 2020 in math.CO, cs.DM, and math.LO
Abstract: We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known to be finite for structures in a non-binary language. Our proof is based on the vector (or product) form of Milliken's Tree Theorem and demonstrates a general method to carry existing results on structures in binary relational languages to higher arities.