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The Erdős–Rado Arrow for Singular Cardinals

Published online by Cambridge University Press:  20 November 2018

Saharon Shelah*
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel, and Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA e-mail:
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We prove in $\text{ZFC}$ that if $\text{cf}\left( \text{ }\lambda \text{ } \right)>{{\aleph }_{0}}$ and ${{2}^{\text{cf}\left( \text{ }\!\!\lambda\!\!\text{ } \right)}}\,<\,\text{ }\!\!\lambda\!\!\text{ }$, then $\text{ }\!\!\lambda\!\!\text{ }\,\to \,{{\left( \text{ }\!\!\lambda\!\!\text{ ,}\,\omega \,\text{+}\,\text{1} \right)}^{2}}$.

Research Article
Copyright © Canadian Mathematical Society 2009


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