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arXiv · 1908.04477

Polarized relations at singulars over successors

Shimon Garti
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Abstract

Erdos, Hajnal and Rado asked whether $\binom{\aleph_{\omega_1}}{\aleph_2}\rightarrow\binom{\aleph_{\omega_1}}{\aleph_0}_2$ and whether $\binom{\aleph_{\omega_1}}{\aleph_2}\rightarrow\binom{\aleph_{\omega_1}}{\aleph_1}_2$. We prove that both relations are independent over ZFC. We shall also prove that $\binom{\mu}{\aleph_2}\rightarrow\binom{\mu}{\aleph_2}_2$ is independent over ZF for some $\mu$ of cofinality $\omega_1$.

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Shimon Garti. 2019-08-13. Polarized relations at singulars over successors. https://doi.org/10.1016/j.disc.2020.111961

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