Natasha Dobrinen, University of Notre Dame
"Infinite-dimensional Ramsey theory for binary relational free amalgamation classes"
We develop infinite-dimensional Ramsey theory for Fraïssé limits of finitely constrained binary relational FAP classes. In our spaces, Souslin-measurable colorings are Ramsey, and for spaces of so-called strong diaries we obtain analogues of the Ellentuck Theorem. Our results are optimal and recover exact big Ramsey degrees via uniform clopen colorings. A key step in the proof is the development of the new notion of an A.3(2)-ideal and a proof that Todorcevic's Abstract Ramsey Theorem still holds when Axiom A.3(2) is replaced by the weaker assumption of an A.3(2)-ideal. This is joint work with Andy Zucker.
MC 5479