Strong Polarized Relations for the Continuum |
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| Authors: | Shimon Garti Saharon Shelah |
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| Institution: | 1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
2. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08854, USA
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| Abstract: | We prove that the strong polarized relation ${\left(\begin{array}{ll} 2^\mu\\ \mu \end{array}\right)\rightarrow \left(\begin{array}{ll} 2^\mu\\ \mu \end{array}\right)^{1,1}_2}$ is consistent with ZFC. We show this for ${\mu = \aleph _0}$ , and for every supercompact cardinal???. We also characterize the polarized relation below the splitting number. |
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