2017/06/25 by Natasha Dobrinen, Dobrinen, Natasha, Dan Hathaway +1 · 1 citation
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1706.08174
19 pages
arxiv created 2019/05/18 · arxiv updated 2019/05/21
We investigate the effects of various forcings on several forms of the Halpern-Läuchli Theorem. For inaccessible κ, we show they are preserved by forcings of size less than κ. Combining this with work of Zhang in \citeZhang17 yields that the polarized partition relations associated with finite products of the κ-rationals are preserved by all forcings of size less than κ over models satisfying the Halpern-Läuchli Theorem at κ. We also show that the Halpern-Läuchli Theorem is preserved by <κ-closed forcings assuming κ is measurable, following some observed reflection properties.