Hostname: page-component-7dd5485656-c8zdz Total loading time: 0 Render date: 2025-10-30T21:51:58.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Namba Forcing and No Good Scale

Published online by Cambridge University Press:  12 March 2014

John Krueger
John Krueger*
Affiliation:
Department of Mathematics, University of North Texas, 1155 Union Circle, #311430 Denton, TX 76203, USA, E-mail: jkrueger@unt.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We develop a version of Namba forcing which is useful for constructing models with no good scale on ℵω . A model is produced in which holds for all finite n ≥ 1, but there is no good scale on ℵω ; this strengthens a theorem of Cummings, Foreman, and Magidor [3] on the non-compactness of square.

Keywords

Good scaleNamba forcing03E3503E04

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 3 , September 2013 , pp. 785 - 802
Copyright
Copyright © Association for Symbolic Logic 2013

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1] Cummings, J., Notes on singular cardinal combinatorics, Notre Dame Journal of Formal Logic, vol. 46 (2005), no. 3, pp. 251–282.CrossRefGoogle Scholar
[2] Cummings, J., Foreman, M., and Magidor, M., Squares, scales, and stationary reflection, Journal of Mathematical Logic, vol. 1 (2001), no. 1, pp. 35–98.CrossRefGoogle Scholar
[3] Cummings, J., Foreman, M., and Magidor, M., The non-compactness of square, this Journal, vol. 68 (2003), no. 2, pp. 637–643.Google Scholar
[4] Cummings, J., Foreman, M., and Magidor, M., Canonical structure in the universe of set theory. I, Annals of Pure and Applied Logic, vol. 129 (2004), no. 1-3, pp. 211–243.CrossRefGoogle Scholar
[5] Cummings, J., Foreman, M., and Magidor, M., Canonical structure in the universe of set theory. II, Annals of Pure and Applied Logic, vol. 142 (2006), no. 1-3, pp. 55–75.CrossRefGoogle Scholar
[6] Foreman, M. and Magidor, M., A very weak square principle, this Journal, vol. 62 (1997), no. 1, pp. 175–196.Google Scholar
[7] Foreman, M., Magidor, M., and Shelah, S., Martins maximum, saturated ideals, andnonregular ultrafilters. I, Annals of Mathematics. Series 2, vol. 127 (1988), no. 2, pp. 1–47.CrossRefGoogle Scholar
[8] Gitik, M. and Shelah, S., On the ⅈ-condition, Israel Journal of Mathematics, vol. 48 (1984), no. 2-3, pp. 148–158.CrossRefGoogle Scholar
[9] Hajnal, A., Juasz, I., and Shelah, S., Splitting strongly almost disjoint families, Transactions of the American Mathematical Society, vol. 295 (1986), no. 1, pp. 369–387.CrossRefGoogle Scholar
[10] Namba, K., Independence proof of (ω, ωα )-distributivity law in complete Boolean algebras, Com-mentarii Mathematici Universitatis Sancti Pauli, vol. 19 (1970), pp. 1–12.Google Scholar
[11] Shelah, S., Cardinal arithmetic, second ed., Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, 1994.CrossRefGoogle Scholar
[12] Shelah, S., Proper and improper forcing, second ed., Perspectives in Mathematical Logic, Springer Verlag, Berlin, 1998.CrossRefGoogle Scholar