Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
Martin Balko
Charles University, Praha 1, Czech RepublicDavid Chodounský
Charles University, Praha 1, Czech Republic; Czech Academy of Sciences, Praha 1, Czech RepublicNatasha Dobrinen
University of Notre Dame, Notre Dame, USAJan Hubička
Charles University, Praha 1, Czech RepublicMatěj Konečný
TU Dresden, Dresden, Germany; Charles University, Praha 1, Czech RepublicLluís Vena
Universitat Politècnica de Catalunya, Barcelona, SpainAndy Zucker
University of Waterloo, Waterloo, Canada
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 satisfying the infinite Ramsey theorem, implying that the automorphism group of the Fraïssé limit has a metrizable universal completion flow.
Cite this article
Martin Balko, David Chodounský, Natasha Dobrinen, Jan Hubička, Matěj Konečný, Lluís Vena, Andy Zucker, Exact big Ramsey degrees for finitely constrained binary free amalgamation classes. J. Eur. Math. Soc. (2024), published online first
DOI 10.4171/JEMS/1507