Journal of Symbolic Logic

A strong polarized relation

Shimon Garti and Saharon Shelah

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We prove that the strong polarized relation (μ+ μ) → (μ+ μ)1,12 is consistent with ZFC, for a singular μ which is a limit of measurable cardinals.

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J. Symbolic Logic, Volume 77, Issue 3 (2012), 766-776.

First available in Project Euclid: 13 August 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E05, 03E55

Partition calculus cardinal arithmetic large cardinals


Garti, Shimon; Shelah, Saharon. A strong polarized relation. J. Symbolic Logic 77 (2012), no. 3, 766--776. doi:10.2178/jsl/1344862161.

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  • G. V. Čudnovskiĭ 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.
  • P. Erdős, A. Hajnal, and R. Rado Partition relations for cardinal numbers, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16(1965), pp. 93–196.
  • P. Erdős and R. Rado A partition calculus in set theory, Bulletin of the American Mathematical Society, vol. 62(1956), pp. 427–489.
  • M. Foreman and A. Hajnal A partition relation for successors of large cardinals, Mathematische Annalen, vol. 325(2003), no. 3, pp. 583–623.
  • M. Gitik and S. Shelah On densities of box products, Topology and its Applications, vol. 88(1998), no. 3, pp. 219–237.
  • R. Laver Making the supercompactness of $\kappa $ indestructible under $\kappa $-directed closed forcing, Israel Journal of Mathematics, vol. 29(1978), no. 4, pp. 385–388.
  • M. Magidor Changing cofinality of cardinals, Polska Akademia Nauk. Fundamenta Mathematicae, vol. 99(1978), no. 1, pp. 61–71.
  • S. Shelah A weak generalization of MA to higher cardinals, Israel Journal of Mathematics, vol. 30(1978), no. 4, pp. 297–306.
  • –––– More on cardinal arithmetic, Archive for Mathematical Logic, vol. 32(1993), no. 6, pp. 399–428.
  • –––– Cardinal arithmetic, Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, New York,1994.
  • –––– A polarized partition relation and failure of GCH at singular strong limit, Fundamenta Mathematicae, vol. 155(1998), no. 2, pp. 153–160.
  • –––– On con($dominating_\lambda > cov_\lambda$(meagre)), preprint.
  • N. H. Williams Combinatorial set theory, studies in logic and the foundations of mathematics, vol. 91, North-Holland, Amsterdam,1977.