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Filters, Cohen sets and consistent extensions of the Erdős-Dushnik-Miller Theorem

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA, E-mail: shelah@sunrise.huji.ac.il E-mail: shelah@math.rutgers.edu
Lee J. Stanley
Affiliation:
Lehigh University, Department of Mathematics, 14 E Packer Avenue, Bethlehem, PA 18015-3174, USA, E-mail: ljs4@lehigh.edu

Abstract

We present two different types of models where, for certain singular cardinals λ of uncountable cofinality, λ → (λ, ω + 1)2, although λ is not a strong limit cardinal, We announce, here, and will present in a subsequent paper, [7], that, for example, consistently, and consistently, .

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2000

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References

[1]Erdős, P., Hajnal, A., Mate, A., and Rado, R., Combinatorial set theory: Partition relations for cardinals, North-Holland, New York, 1984.Google Scholar
[2]Sheiah, S., Borel sets with large squares, Fundamenta Mathematica, submitted.Google Scholar
[3]Sheiah, S., Was Sierpinski right, I?, Israel Journal of Mathematics, vol. 62 (1988), pp. 335380, paper #276.Google Scholar
[4]Sheiah, S., On for α < ω2, Logic colloquium '90 (Oikkonen, J. and Väänänen, J., editors), Lecture Notes in Logic, no. 2, Springer-Verlag, Berlin, 1993, ASL summer meeting in Helsinki, pp. 281289.Google Scholar
[5]Sheiah, S., Cardinal arithmetic, Oxford Logic Guides, no. 29, Oxford University Press, Oxford, 1994.Google Scholar
[6]Shelah, S. and Stanley, L., A theorem and some consistency results in partition calculus, Annals of Pure and Applied Logic, vol. 36 (1987), pp. 119152.CrossRefGoogle Scholar
[7]Shelah, S. and Stanley, L., Consistent negative and positive partition relations for singular cardinals of uncountable cofinality, in preparation.Google Scholar
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