A partition relation using strongly compact cardinals

Shelah, Saharon

doi:10.1090/S0002-9939-02-06789-8

A partition relation using strongly compact cardinals
HTML articles powered by AMS MathViewer

by Saharon Shelah PDF

Proc. Amer. Math. Soc. 131 (2003), 2585-2592 Request permission

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

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
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
Saharon Shelah, Notes on combinatorial set theory, Israel J. Math. 14 (1973), 262–277. MR 327522, DOI 10.1007/BF02764885
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
Saharon Shelah, On $\textrm {CH}+2^{\aleph _1}\to (\alpha )^2_2$ for $\alpha <\omega _2$, Logic Colloquium ’90 (Helsinki, 1990) Lecture Notes Logic, vol. 2, Springer, Berlin, 1993, pp. 281–289. MR 1279847
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, DOI 10.4064/fm-166-1-2-1-82