A polarized partition relation for cardinals of countable cofinality
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- by Albin L. Jones
- Proc. Amer. Math. Soc. 136 (2008), 1445-1449
- DOI: https://doi.org/10.1090/S0002-9939-07-09143-5
- Published electronically: November 30, 2007
Abstract:
We prove that if $\operatorname {cf}{\kappa } = \omega$ and $\lambda = 2^{<\kappa }$, then \[ \left ( \begin {matrix} \lambda ^+ \lambda \end {matrix} \right ) \to \left ( \begin {matrix} \lambda ^+ & \alpha \lambda & \kappa \end {matrix} \right )^{\!\!\!1,1} \] for all $\alpha < \omega _1$. This polarized partition relation holds if for every partition $\lambda \times \lambda ^+ = K_0 \cup K_1$ either there are $B_0 \in [\lambda ]^{\lambda }$ and $A_0 \in [\lambda ^+]^{\lambda ^+}$ with $B_0 \times A_0 \subseteq K_0$ or there are $B_1 \in [\kappa ]^{\lambda }$ and $A_1 \in [\alpha ]^{\lambda ^+}$ with $B_1 \times A_1 \subseteq K_1$.References
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Bibliographic Information
- Albin L. Jones
- Affiliation: 2153 Oakdale Rd., Pasadena, Maryland 21122
- MR Author ID: 662270
- Email: alj@mojumi.net
- Received by editor(s): October 13, 2006
- Received by editor(s) in revised form: February 15, 2007
- Published electronically: November 30, 2007
- Communicated by: Julia Knight
- © Copyright 2007 Albin L. Jones
- Journal: Proc. Amer. Math. Soc. 136 (2008), 1445-1449
- MSC (2000): Primary 03E05, 05D10; Secondary 05A18
- DOI: https://doi.org/10.1090/S0002-9939-07-09143-5
- MathSciNet review: 2367118