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Open and solved problems concerning polarized partition relations

Shimon Garti; Saharon Shelah — 2016

Fundamenta Mathematicae

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 α there exists a forcing notion ℙ such that the strong polarized relation $(\binom{ℵ_{α + 1}}{ℵ_{α}}) \to {(\binom{ℵ_{α + 1}}{ℵ_{α}})}_{2}^{1, 1}$ holds in $V^{ℙ}$ .

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