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Forcing many positive polarized partition relations between a cardinal and its powerset

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah  and
Lee J. Stanley
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel and Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway NJ 08854-8019, USA, E-mail: shelah@math.huji.ac.il., E-mail: shelah@math.rutgers.edu
Lee J. Stanley
Affiliation:
Department of Mathematics, Lehigh University, 14 E. Packer Avenue, Bethlehem, PA, 18015-3174, USA, E-mail: ljs4@lehigh.edu
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Abstract

A fairly quotable special, but still representative, case of our main result is that for 2 ≤ n < ω, there is a natural number m(n) such that, the following holds. Assume GCH: If λ < μ are regular, there is a cofinality preserving forcing extension in which 2λ = μ and, for all σ < λ ≤ κ < η such that η(+m(n)−+) ≤ μ,

This generalizes results of [3], Section 1. and the forcing is a “many cardinals” version of the forcing there.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1359 - 1370
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

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[7]Shelah, S., Was Sierpiński right, IV?, submitted to this Journal.Google Scholar