Logic Seminar

Spencer UngerUniversity of Toronto
Ramsey theory of trees

Friday, December 2, 2022 - 2:45pm
Malott 206

We make several observations about the infinite dimensional Ramsey theory of trees. To start we define a weakening of a Ramsey space and give a natural class of examples these spaces which do not satisfy Todorcevic's axioms (in particular the amalgamation axiom fails). Motivated by these examples, we give a classical proof of a version of the Halpern-Lauchli theorem which allows us to analyze spaces of copies of the rationals. This is joint work with Stevo Todorcevic.