Exact big Ramsey degrees via coding trees

Abstract

We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fraïssé limit of each such class admits a big Ramsey structure. Consequently, the automorphism group of each such Fraïssé limit has a metrizable universal completion flow.