2000 character limit reached
Infinite-dimensional Ramsey theory for binary free amalgamation classes (2303.04246v2)
Published 7 Mar 2023 in math.LO and math.CO
Abstract: We develop infinite-dimensional Ramsey theory for Fra\"iss\'e limits of finitely constrained free amalgamation classes in finite binary languages. We show that our approach is optimal and in particular, recovers the exact big Ramsey degrees proved in [2] for these structures. A crucial step in the work develops the new notion of an A.3(2)-ideal and shows that Todorcevic's Abstract Ramsey Theorem holds when Axiom A.3(2) is replaced by the weaker assumption of an A.3(2)-ideal.