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

Saharon Shelah; Lee J. Stanley

doi:10.2307/2695112

Published online by Cambridge University Press: 12 March 2014

Saharon Shelah and

Lee J. Stanley

Show author details

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

Corresponding

E-mail address:

shelah@math.huji.ac.il. ;

shelah@math.rutgers.edu ;

ljs4@lehigh.edu

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.

References

[1]Komjath, P. and Shelah, S., On Taylor's problem, Acta Mathematica Hungarica, vol. 70 (1996), pp. 217–225.CrossRef Google 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.CrossRef Google 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.Google 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.CrossRef Google Scholar

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

Please list any fees and grants from, employment by, consultancy for, shared ownership in or any close relationship with, at any time over the preceding 36 months, any organisation whose interests may be affected by the publication of the response. Please also list any non-financial associations or interests (personal, professional, political, institutional, religious or other) that a reasonable reader would want to know about in relation to the submitted work. This pertains to all the authors of the piece, their spouses or partners.

Article contents

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

Abstract

Access options

References

Full text views

This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

Article contents

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

Abstract

Access options

References

Full text views

Send article to Kindle

Send article to Dropbox

Send article to Google Drive

Reply to: Submit a response

Your details

Conflicting interests