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Open and solved problems concerning polarized partition relations

Volume 234 / 2016

Shimon Garti, Saharon Shelah 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 ${\rm \bf V}^{\mathbb {P}}$.

Authors

  • Shimon GartiInstitute of Mathematics
    The Hebrew University of Jerusalem
    Jerusalem 91904, Israel
    e-mail
  • Saharon ShelahInstitute of Mathematics
    The Hebrew University of Jerusalem
    Jerusalem 91904, Israel
    and
    Department of Mathematics
    Rutgers University
    New Brunswick, NJ 08854, U.S.A.
    e-mail

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