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

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Abstract | References | Similar Articles | Additional Information

Abstract: If is strongly compact and and is regular (or alternatively cf , then holds for .

**[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**

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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:
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