# An alternate proof of the Halpern-Läuchli Theorem in one dimension

Set theory seminarFriday, September 12, 201410:00 amGC 5382

# An alternate proof of the Halpern-Läuchli Theorem in one dimension

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.