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Proceedings of the American Mathematical Society
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A partition relation using strongly compact cardinals

Author(s): Saharon Shelah
Journal: Proc. Amer. Math. Soc. 131 (2003), 2585-2592.
MSC (2000): Primary 03E02
Posted: December 30, 2002
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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:

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P. Erdos, A. Hajnal: Unsolved problems in set theory, Proc. Symp. Pure Math. 8, Providence, Rhode Island, 17-48. MR 43:6101

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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

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Saharon Shelah. Notes on combinatorial set theory. Israel Journal of Mathematics, 14:262-277, 1973. MR 48:5864

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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

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Saharon Shelah. On $CH + 2^{\aleph _{1}}\rightarrow (\alpha
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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


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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: 10.1090/S0002-9939-02-06789-8
PII: S 0002-9939(02)06789-8
Received by editor(s): January 16, 2002
Received by editor(s) in revised form: March 12, 2002
Posted: 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.
Copyright of article: Copyright 2002, American Mathematical Society


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