Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-25T17:43:51.905Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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.)

References

REFERENCES

[1]Komjath, P. and Shelah, S., On Taylor's problem, Acta Mathematica Hungarica, vol. 70 (1996), pp. 217–225.CrossRefGoogle Scholar
[2]Rabus, M. and Shelah, S., Consistency of partition relations, submitted to Annals of Pure and Applied Logic.Google Scholar
[3]Shelah, S., Was Sierpiński right, I?, Israel Journal of Mathematics, vol. 62 (1988), pp. 355–380.CrossRefGoogle Scholar
[4]Shelah, S., Strong partition relations below the power set: Consistency, was Sierpinski right, II?, Sets, graphs, and numbers: Proceedings of the conference on set theory and its applications in honor of A. Hajnal and V. T. Sos (Budapest), Colloquia Mathematica Societatis, vol. 60, Janos Bolyai, 01 1991, pp. 637–638.Google Scholar
[5]Shelah, S., Consistency of positive partition theorems for graphs and models, Set theory and its applications (Toronto, ON, 1987) (Steprans, J. and Watson, S., editors), Lecture Notes in Mathematics, vol. 1401, Springer, Berlin-New York, 1989, pp. 167–193.CrossRefGoogle Scholar
[6]Shelah, S., Was Sierpinski right, III? Can continuum–c.c. times c.c.c. be continuum–c.c.?, Annals of Pure and Applied Logic, vol. 78 (1996), pp. 259–269.CrossRefGoogle Scholar
[7]Shelah, S., Was Sierpiński right, IV?, submitted to this Journal.Google Scholar