Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-01T13:23:36.694Z Has data issue: false hasContentIssue false
  • English
  • Français

Forcing disabled

Published online by Cambridge University Press:  12 March 2014

M. C. Stanley
M. C. Stanley*
Affiliation:
Department of Mathematics, San Jose State University, San Jose, California 95192, E-mail: Stanley@math.sjsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

It is proved (Theorem 1) that if 0# exists, then any constructible forcing property which over L adds no reals, over V collapses an uncountable L-cardinal to cardinality ω. This improves a theorem of Foreman, Magidor, and Shelah. Also, a method for approximating this phenomenon generically is found (Theorem 2). The strategy is first to reduce the problem of ‘disabling’ forcing properties to that of specializing certain trees in a weak sense.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 4 , December 1992 , pp. 1153 - 1175
Copyright
Copyright © Association for Symbolic Logic 1992

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

[D]Dodd, A. J., The core model, London Mathematical Society Lecture Note Series, vol. 61, Cambridge University Press, Cambridge, 1982.CrossRefGoogle Scholar
[FMS]Foreman, M., Magidor, M., and Shelah, S., 0# and some forcing principles, this Journal, vol. 51 (1986), pp. 39–46.Google Scholar