Open and solved problems concerning polarized partition relations
Volume 234 / 2016
Fundamenta Mathematicae 234 (2016), 1-14
MSC: Primary 03E05; Secondary 03E35.
DOI: 10.4064/fm763-10-2015
Published online: 11 February 2016
Abstract
We list some open problems concerning the polarized partition relation. We solve a couple of them, by showing that for every limit non-inaccessible ordinal $\alpha $ there exists a forcing notion $\mathbb {P}$ such that the strong polarized relation $\binom {\aleph _{\alpha +1}}{\aleph _\alpha } \rightarrow \binom {\aleph _{\alpha +1}}{\aleph _\alpha }^{1,1}_2$ holds in ${\rm \bf V}^{\mathbb {P}}$.
