Andy Zucker, Department of Pure Mathematics, University of Waterloo
"Polish partition principles and the Halpern-Lauchli theorem"
The Halpern-Lauchli theorem is a partition theorem about products of trees. While the theorem is entirely combinatorial in nature, one proof due to Leo Harrington uses some ideas from forcing. This proof uses the Erdos-Rado theorem to analyze a sufficiently rich forcing poset which is built using the trees in question. Notably, there is no need to actually pass to the generic extension in the course of the proof. In recent joint work with Chris Lambie-Hanson, we reimagine Harrington's proof by actually passing to the generic extension. In so doing, we isolate and investigate a consistent partition principle about products of perfect Polish spaces.
MC 5403