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
Published electronically: December 30, 2002
MathSciNet review: 1974659
Full-text PDF Free Access

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. Erdős and A. Hajnal, Unsolved problems in set theory, Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 17–48. MR 0280381
  • [BHT93] James E. Baumgartner, András Hajnal, and Stevo Todorčević, Extensions of the Erdős-Rado theorem, Finite and infinite combinatorics in sets and logic (Banff, AB, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 411, Kluwer Acad. Publ., Dordrecht, 1993, pp. 1–17. MR 1261193
  • [Sh:26] Saharon Shelah, Notes on combinatorial set theory, Israel J. Math. 14 (1973), 262–277. MR 0327522
  • [Sh:420] Saharon Shelah, Advances in cardinal arithmetic, Finite and infinite combinatorics in sets and logic (Banff, AB, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 411, Kluwer Acad. Publ., Dordrecht, 1993, pp. 355–383. MR 1261217
  • [Sh:424] Saharon Shelah, On 𝐶𝐻+2^{ℵ₁}→(𝛼)²₂ for 𝛼<𝜔₂, Logic Colloquium ’90 (Helsinki, 1990) Lecture Notes Logic, vol. 2, Springer, Berlin, 1993, pp. 281–289. MR 1279847
  • [Sh:666] Saharon Shelah, On what I do not understand (and have something to say). I, Fund. Math. 166 (2000), no. 1-2, 1–82. Saharon Shelah’s anniversary issue. MR 1804704

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