Geodesic
The Erdős–Rado Arrow for Singular Cardinals
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 127-131

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\text{ }\!\!\lambda\!\!\text{ }\,\to \,{{\left( \text{ }\!\!\lambda\!\!\text{ ,}\,\omega \,\text{+}\,\text{1} \right)}^{2}}$ .
DOI : 10.4153/CMB-2009-015-8
Mots-clés : 03E20, set theory, partition calculus 
Shelah, Saharon. The Erdős–Rado Arrow for Singular Cardinals. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 127-131. doi: 10.4153/CMB-2009-015-8
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[1] [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] [2] Shelah, S., A note on cardinal exponentiation. J. Symbolic Logic 45(1980), no. 1, 56–66. Google Scholar

[3] [3] Shelah, S., Cardinal Arithmetic. Oxford Logic Guides 29, Oxford University Press, New York, 1994. Google Scholar

[4] [4] Shelah, S., Applications of PCF theory. J. Symbolic Logic 65(2000), no. 4, 1624–1674. Google Scholar

[5] [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

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