Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
Logic
2025-06-09 v3 Combinatorics
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 Fra\"iss\'e limit of each such class admits a strong big Ramsey structure, implying that the automorphism group of the Fra\"iss\'e limit has a metrizable universal completion flow.
Cite
@article{arxiv.2110.08409,
title = {Exact big Ramsey degrees for finitely constrained binary free amalgamation classes},
author = {Martin Balko and David Chodounský and Natasha Dobrinen and Jan Hubička and Matěj Konečný and Lluis Vena and Andy Zucker},
journal= {arXiv preprint arXiv:2110.08409},
year = {2025}
}
Comments
Revised version; formerly titled "Exact big Ramsey degrees via coding trees."