Tag Archives: polarized partition relation

This post continues the study of the cardinal invariant $\mathfrak{p}$. We refer the reader to a previous post for all the needed background. For ordinals $\alpha ,{\alpha }_0,{\alpha }_1,\beta ,{\beta }_0,{\beta }_1$, the polarized partition relation $$\left(\begin{array}{c}\alpha \\ \beta \end{array}\right)\to \left(\begin{array}{cc}{\alpha }_0& {\alpha }_1\\ {\beta }_0& {\beta }_1\end{array}\right)$$ asserts that for every coloring $f:\alpha \times \beta \to 2$, (at least) … Continue reading →