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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
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Abstract

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

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

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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