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The Erdős–Rado Arrow for Singular Cardinals

Published online by Cambridge University Press:  20 November 2018

Saharon Shelah
Saharon Shelah*
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel, and Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA e-mail: shelah@math.huji.ac.il
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Abstract

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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 $\text{ }\!\!\lambda\!\!\text{ }\,\to \,{{\left( \text{ }\!\!\lambda\!\!\text{ ,}\,\omega \,\text{+}\,\text{1} \right)}^{2}}$.

Keywords

03E20set theorypartition calculus
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 127 - 131
Copyright
Copyright © Canadian Mathematical Society 2009

References

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