Journal of Symbolic Logic

A strong polarized relation

Shimon Garti and Saharon Shelah

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 13 August 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1344862161

Digital Object Identifier
doi:10.2178/jsl/1344862161

Mathematical Reviews number (MathSciNet)
MR2987137

Zentralblatt MATH identifier
1270.03076

Subjects
Primary: 03E05, 03E55

Keywords
Partition calculus cardinal arithmetic large cardinals

Citation

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


Export citation

References

  • 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.