# 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

### 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.

Posted by on August 23rd, 2014