Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-31T19:38:18.098Z Has data issue: false hasContentIssue false
  • English
  • Français

A universal extender model without large cardinals in V

Published online by Cambridge University Press:  12 March 2014

William Mitchell  and
Ralf Schindler
William Mitchell
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105., USA, E-mail: [email protected]
Ralf Schindler
Affiliation:
Institut für Mathematische Logik, und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract.

We construct, assuming that there is no inner model with a Woodin cardinal but without any large cardinal assumption, a model Kc which is iterable for set length iterations, which is universal with respect to all weasels with which it can be compared, and (assuming GCH) is universal with respect to set sized premice.

Keywords

Set theorycore modelslarge cardinals
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 2 , June 2004 , pp. 371 - 386
Copyright
Copyright © Association for Symbolic Logic 2004

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]Jech, Tom, Set theory, Academic Press, Inc., San Diego, 1978.Google Scholar
[2]Jensen, Ronald, Addendum to “A new fine structure for higher core models”, handwritten notes, Berlin, 1997.Google Scholar
[3]Mitchell, William and Steel, John, Fine structure and iteration trees, Lecture Notes in Logic, vol. 3, Springer, 1994.CrossRefGoogle Scholar
[4]Schindler, Ralf, The core model for almost linear iterations, Annals of Pure and Applied Logic, vol. 116 (2002), pp. 205–272.CrossRefGoogle Scholar
[5]Schindler, Ralf, Steel, John, and Zeman, Martin, Deconstructing inner model theory, this Journal, vol. 67 (2002), pp. 721–736.Google Scholar
[6]Steel, John, The core model iterability problem, Lecture Notes in Logic, vol. 8, Springer, 1996.CrossRefGoogle Scholar