Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T18:26:06.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Polarized partition relations

Published online by Cambridge University Press:  12 March 2014

James E. Baumgartner and
Andras Hajnal
James E. Baumgartner
Affiliation:
Dartmouth College, Department of Mathematics, Hanover, NH 03755, USA, E-mail: james.baumgartner@dartmouth.edu
Andras Hajnal
Affiliation:
Rutgers University, Department of Mathematics, Piscataway, N.J. 08854, USA, E-mail: ahajnal@math.rutgers.edu
Get accessRights & Permissions [Opens in a new window]

Abstract

It is shown that for any cardinal κ, , and if κ is weakly compact then .

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001, pp. 811 - 821
Copyright
Copyright © Association for Symbolic Logic 2001

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]Baumgartner, J., Ineffability properties of cardinals I, Proceedings of the colloquium on infinite and finite sets (Hungary), 1973, pp. 109–130.Google Scholar
[2]Baumgartner, J., Hajnal, A., and Todorčević, , Extensions of the Erdős-Rado theorem, Finite and infinite sets (Proceedings of the Banff conference), 1991.Google Scholar
[3]Baumgartner, J. and Shelah, S., Remarks on superatomic Boolean algebras, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 109–129.CrossRefGoogle Scholar
[4]Choodnovsky, G. V., Combinatorial properties of compact cardinals, Proceedings of the colloquium on infinite and finite sets, 1973, pp. 289–306.Google Scholar
[5]Erdős, P. and Hajnal, A., Unsolved and solved problems in set theory, Proceedings of the Tarski symposium (Proceedings of the symposium on pure mathematics), 1971, pp. 269–287.Google Scholar
[6]Erdős, P., Hajnal, A., and Rado, R., Partition relations for cardinal numbers, Acta Mathematika Hungarica, vol. 16 (1965), pp. 93–196.CrossRefGoogle Scholar
[7]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
[8]Hajnal, A., On some combinatorial problems involving large cardinals, Fundamenta Mathematicae, vol. 69 (1970), pp. 39–53.CrossRefGoogle Scholar
[9]Kanamori, A., On Silver's and related principles, Proceedings of the logic colloquium '80 (North Holland) (van Dalen, D., Lascar, D., and Smiley, J., editors), 1982, pp. 153–172.Google Scholar
[10]Prikry, K., On a problem of Erdős, Hajnal, and Rado, Discrete Mathematics, vol. 2 (1972), pp. 51–59.CrossRefGoogle Scholar
[11]Shelah, S., A polarized partition relation and failure ofGCHat singular strong limit, Fundamenta Mathematicae, vol. 155 (1998), pp. 153–160, (pub. 586).CrossRefGoogle Scholar
[12]Wolfsdorf, K., Der Beweis eines Satzes von G. Choodnovsky, Archive for Mathematical Logic, vol. 20 (1980), pp. 161–171.CrossRefGoogle Scholar