Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-20T05:19:21.258Z Has data issue: false hasContentIssue false
  • English
  • Français

Increasing δ21 and Namba-style forcing

Published online by Cambridge University Press:  12 March 2014

Richard Ketchersid ,
Paul Larson  and
Jindřich Zapletal
Richard Ketchersid
Affiliation:
Department of Mathematics & Statistics, Miami University, Oxford, OH 45056, USA. E-mail: ketchero@muohio.edu
Paul Larson
Affiliation:
Department of Mathematics & Statistics, Miami University, Oxford, OH 45056, USA. E-mail: larsonpb@muohio.edu
Jindřich Zapletal
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, FL 32611-8105, USA. E-mail: jinzap@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We isolate a forcing which increases the value of while preserving ω1 under the assumption that there is a precipitous ideal on ω1 and a measurable cardinal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1372 - 1378
Copyright
Copyright © Association for Symbolic Logic 2007

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]Foreman, Matthew, Magidor, Menachem, and Shelah, Saharon, Martins Maximum, saturated ideals, and non-regular ultrafilters I, Annals of Mathematics, vol. 127 (1988), pp. 1–47.CrossRefGoogle Scholar
[2]Jech, Thomas, Set theory, Academic Press, San Diego, 1978.Google Scholar
[3]Jech, Thomas, Magidor, Menachem, Mitchell, William, and Prikry, Karel, Precipitous ideals, this Journal, vol. 45 (1980), pp. 1–8.Google Scholar
[4]Jensen, Ronald, Making cardinals ω-cofinal, handwritten notes, 1990s.Google Scholar
[5]Namba, Kanji, Independence proof of a distributive law in complete Boolean algebras, Commentarii Mathematici Universitatis Sancti Pauli, vol. 19 (1970), pp. 1–12.Google Scholar
[6]Woodin, Hugh, The axiom of determinacy, forcing axioms and the nonstationary ideal, Walter de Gruyter, New York, 1999.CrossRefGoogle Scholar
[7]Zapletal, Jindřich, The nonstationary ideal and the other sigma-ideals on omega one, Transactions of the American Mathematical Society, vol. 352 (2000), pp. 3981–3993.CrossRefGoogle Scholar
[8]Zapletal, Jindřich, Forcing idealized, Cambridge University Press, 2007, to appear.Google Scholar