Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A partition relation using strongly compact cardinals


Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 131 (2003), 2585-2592
MSC (2000): Primary 03E02
DOI: https://doi.org/10.1090/S0002-9939-02-06789-8
Published electronically: December 30, 2002
MathSciNet review: 1974659
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If $\kappa $ is strongly compact and $\lambda > \kappa $ and $\lambda $is regular (or alternatively cf $(\lambda ) \ge \kappa )$, then $\left (2^{<\lambda }\right )^{+} \rightarrow (\lambda + \zeta )^{2}_{\theta }$ holds for $\zeta ,\theta < \kappa $.


References [Enhancements On Off] (What's this?)

  • [ERDHAJ] P. Erdos, A. Hajnal: Unsolved problems in set theory, Proc. Symp. Pure Math. 8, Providence, Rhode Island, 17-48. MR 43:6101
  • [BHT93] James Baumgartner, Andras Hajnal, and Stevo Todorcevic. Extensions of the Erdos-Rado Theorems. In Finite and Infinite Combinatorics in Set Theory and Logic, pages 1-18. Kluwer Academic Publishers, 1993. N.W. Sauer et. al. eds. MR 95c:03111
  • [Sh:26] Saharon Shelah. Notes on combinatorial set theory. Israel Journal of Mathematics, 14:262-277, 1973. MR 48:5864
  • [Sh:420] Saharon Shelah. Advances in Cardinal Arithmetic. In Finite and Infinite Combinatorics in Sets and Logic, pages 355-383. Kluwer Academic Publishers, 1993. N.W. Sauer et al (eds.). MR 95h:03112
  • [Sh:424] Saharon Shelah. On $CH + 2^{\aleph _{1}}\rightarrow (\alpha )^{2}_{2}$ for $\alpha <\omega _{2}$. In Logic Colloquium'90. ASL Summer Meeting in Helsinki, volume 2 of Lecture Notes in Logic, pages 281-289. Springer Verlag, 1993. math.LO/9308212 MR 95m:03098
  • [Sh:666] Saharon Shelah. On what I do not understand (and have something to say). Fundamenta Mathematicae, 166:1-82, 2000. math.LO/9906113 MR 2002a:03091

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E02

Retrieve articles in all journals with MSC (2000): 03E02


Additional Information

Saharon Shelah
Affiliation: Institute of Mathematics, The Hebrew University, Jerusalem, Israel – and – Department of Mathematics, Rutgers University, New Brunswick, New Jersey
Email: shelah@math.huji.ac.il

DOI: https://doi.org/10.1090/S0002-9939-02-06789-8
Received by editor(s): January 16, 2002
Received by editor(s) in revised form: March 12, 2002
Published electronically: December 30, 2002
Additional Notes: The author thanks Alice Leonhardt for the beautiful typing
Research of the author was partially supported by the United States-Israel Binational Science Foundation. Publication 761
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society