An alternate proof of the Halpern-Läuchli Theorem in one dimension
The CUNY Graduate Center
I will present a new proof of the strong subtree version of the Halpern-Läuchli Theorem, using an ultrafilter on $\omega$. The one dimensional Halpern-Läuchli Theorem states that for every finite partition of an infinite, finitely branching tree $T$, there is one piece $P$ of the partition and a strong subtree $S$ of $T$ such that $S \subseteq P$. This will cover the one dimensional case, with hopes that the proof can be extended to cover a product of trees.
Erin Carmody is a visiting assistant professor at Nebraska Wesleyan University. Her research is in the field of set theory. She received her doctorate in 2015 under the supervision of Joel David Hamkins.