Forcing and the Halpern-Läuchli Theorem

Natasha Dobrinen, Dan Hathaway

Published 2017-06-25Version 1

We will show the various effects that forcing has on the Halpern-L\"auchli Theorem. We will show that the somewhere dense version of the theorem at an inaccessible $\kappa$ is preserved by forcings of size $< \kappa$ and, assuming $\kappa$ is measurable, by ${{<}\kappa}$-closed forcings.