2025/03/24 by Chodounský, David, Eskew, Monroe, Weinert, Thilo · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2503.18727
We investigate big Ramsey degrees of finite substructures of the universal countable homogeneous meet-tree and its binary variant. We prove that structures containing antichains have infinite big Ramsey degrees, and the big Ramsey degree of a 2-element chain is at least 8 and 7 for the binary variant. We deduce that the generic C-relation does not have finite big Ramsey degrees.