Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-15T05:30:14.706Z Has data issue: false hasContentIssue false
  • English
  • Français

A strong polarized relation

Published online by Cambridge University Press:  12 March 2014

Shimon Garti and
Saharon Shelah
Shimon Garti
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel, E-mail: shimon.garty@mail.huji.ac.il
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel and, Department of Mathematics, Rutgers University New Brunswick, NJ 08854, USA, E-mail: shelah@math.huji.ac.il, URL: http://www.math.rutgers.edu/~shelah
Get accessRights & Permissions [Opens in a new window]

Abstract

We prove that the strong polarized relation is consistent with ZFC, for a singular μ which is a limit of measurable cardinals.

Keywords

Partition calculuscardinal arithmeticlarge cardinals

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 3 , September 2012, pp. 766 - 776
Copyright
Copyright © Association for Symbolic Logic 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1] Čudnovskiĭ, G. V., Combinatorial properties of compact cardinals, Infinite and finite sets (Colloquium, Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, North-Holland, Amsterdam, 1975, pp. 289–306. Colloquium of the János Bolyai Mathematical Society. Vol. 10.Google Scholar
[2] Erdős, P., Hajnal, A., and Rado, R., Partition relations for cardinal numbers, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16 (1965), pp. 93–196.CrossRefGoogle Scholar
[3] Erdős, P. and Rado, R., A partition calculus in set theory, Bulletin of the American Mathematical Society, vol. 62 (1956), pp. 427–489.CrossRefGoogle Scholar
[4] Foreman, M. and Hajnal, A., A partition relation for successors of large cardinals, Mathematische Annalen, vol. 325 (2003), no. 3, pp. 583–623.CrossRefGoogle Scholar
[5] Gitik, M. and Shelah, S., On densities of box products, Topology and its Applications, vol. 88 (1998), no. 3, pp. 219–237.CrossRefGoogle Scholar
[6] Laver, R., Making the supercompactness of k indestructible under k-directed closed forcing, Israel Journal of Mathematics, vol. 29 (1978), no. 4, pp. 385–388.CrossRefGoogle Scholar
[7] Magidor, M., Changing cofinality of cardinals, Polska Akademia Nauk. Fundamenta Mathematicae, vol. 99 (1978), no. 1, pp. 61–71.CrossRefGoogle Scholar
[8] Shelah, S., A weak generalization of MA to higher cardinals, Israel Journal of Mathematics, vol. 30 (1978), no. 4, pp. 297–306.CrossRefGoogle Scholar
[9] Shelah, S., More on cardinal arithmetic, Archive for Mathematical Logic, vol. 32 (1993), no. 6, pp. 399–428.CrossRefGoogle Scholar
[10] Shelah, S., Cardinal arithmetic, Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, New York, 1994.CrossRefGoogle Scholar
[11] Shelah, S., A polarized partition relation and failure of GCH at singular strong limit, Fundamenta Mathematicae, vol. 155 (1998), no. 2, pp. 153–160.CrossRefGoogle Scholar
[12] Shelah, S., On con(dominatingλ > covλ(meagre)), preprint.+covλ(meagre)),+preprint.>Google Scholar
[13] Williams, N. H., Combinatorial set theory, studies in logic and the foundations of mathematics, vol. 91, North-Holland, Amsterdam, 1977.CrossRefGoogle Scholar