2020/08/01 by Balko, Martin, Chodounský, David, Hubička, Jan +2 · 1 citation
#05C05 #05C55 #05C65 #05D10 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #Logic (math.LO)
paper · doi:10.48550/arxiv.2008.00268
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.