Hostname: page-component-76c49bb84f-c7tcl Total loading time: 0 Render date: 2025-07-10T09:44:13.611Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Information

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

References

[1] Erdős, P., Hajnal, A., Maté, A., and Rado, R., Combinatorial set theory: partition relations for cardinals. Studies in Logic and the Foundations of Mathematics 106, North Holland Publishing Co, Amsterdam, 1984.Google Scholar
[2] Shelah, S., A note on cardinal exponentiation. J. Symbolic Logic 45(1980), no. 1, 56–66.Google Scholar
[3] Shelah, S., Cardinal Arithmetic. Oxford Logic Guides 29, Oxford University Press, New York, 1994.Google Scholar
[4] Shelah, S., Applications of PCF theory. J. Symbolic Logic 65(2000), no. 4, 1624–1674.Google Scholar
[5] Shelah, S. and Stanley, L., Filters, Cohen sets and consistent extensions of the Erdős–Dushnik–Miller theorem. J. Symbolic Logic 65(2000), no. 1, 259–271.Google Scholar