Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T19:39:55.608Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak Compactness and No Partial Squares

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 present a characterization of weakly compact cardinals in terms of generalized stationarity. We apply this characterization to construct a model with no partial square sequences.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 3 , September 2011 , pp. 1035 - 1060
Copyright
Copyright © Association for Symbolic Logic 2011

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]Baumgartner, J., Iterated forcing, Surveys in set theory, Cambridge University Press, 1983, pp. 159.Google Scholar
[2]Foreman, M. and Todorčević, S., A new Löwenheim-Skolem theorem, Transactions of the American Mathematical Society, vol. 357 (2005), no. 5, pp. 1693–1715.CrossRefGoogle Scholar
[3]Hauser, K., Indescribable cardinals and elementary embeddings. this Journal, vol. 56 (1991), pp. 439–457.Google Scholar
[4]Jech, T., Set theory, the third millennium revised and expanded ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Google Scholar
[5]Magidor, M., Reflecting stationary sets, this Journal, vol. 47 (1982), no. 4, pp. 755–771.Google Scholar
[6]Sakai, H., Remark on partial square, preprint, 2009.Google Scholar
[7]Schimmerling, E. and Zeman, M., Square in core models, The Bulletin of Symbolic Logic, vol. 7 (2001), no. 3, pp. 305–314.CrossRefGoogle Scholar
[8]Shelah, S., Reflecting stationary sets and successors of singular cardinals, Archive for Mathematical Logic, vol. 31 (1991), pp. 25–53.CrossRefGoogle Scholar
[9]Shelah, S., Proper and improper forcing, second ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin. 1998.CrossRefGoogle Scholar