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A strong polarized relation

Published online by Cambridge University Press:  12 March 2014

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

Abstract

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

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2012

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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. 289306. 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. 93196.CrossRefGoogle Scholar
[3] Erdős, P. and Rado, R., A partition calculus in set theory, Bulletin of the American Mathematical Society, vol. 62 (1956), pp. 427489.CrossRefGoogle Scholar
[4] Foreman, M. and Hajnal, A., A partition relation for successors of large cardinals, Mathematische Annalen, vol. 325 (2003), no. 3, pp. 583623.CrossRefGoogle Scholar
[5] Gitik, M. and Shelah, S., On densities of box products, Topology and its Applications, vol. 88 (1998), no. 3, pp. 219237.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. 385388.CrossRefGoogle Scholar
[7] Magidor, M., Changing cofinality of cardinals, Polska Akademia Nauk. Fundamenta Mathematicae, vol. 99 (1978), no. 1, pp. 6171.Google Scholar
[8] Shelah, S., A weak generalization of MA to higher cardinals, Israel Journal of Mathematics, vol. 30 (1978), no. 4, pp. 297306.CrossRefGoogle Scholar
[9] Shelah, S., More on cardinal arithmetic, Archive for Mathematical Logic, vol. 32 (1993), no. 6, pp. 399428.CrossRefGoogle Scholar
[10] Shelah, S., Cardinal arithmetic, Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, New York, 1994.Google Scholar
[11] Shelah, S., A polarized partition relation and failure of GCH at singular strong limit, Fundamenta Mathematicae, vol. 155 (1998), no. 2, pp. 153160.Google 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.Google Scholar
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