Journal of Symbolic Logic

Killing the $GCH$ everywhere with a single real

Sy-David Friedman and Mohammad Golshani

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Shelah—Woodin [10] investigate the possibility of violating instances of GCH through the addition of a single real. In particular they show that it is possible to obtain a failure of CH by adding a single real to a model of GCH, preserving cofinalities. In this article we strengthen their result by showing that it is possible to violate GCH at all infinite cardinals by adding a single real to a model of GCH. Our assumption is the existence of an $H(\kappa^{+3})$-strong cardinal; by work of Gitik and Mitchell [6] it is known that more than an $H(\kappa^{++})$-strong cardinal is required.

Article information

J. Symbolic Logic, Volume 78, Issue 3 (2013), 803-823.

First available in Project Euclid: 6 January 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Friedman, Sy-David; Golshani, Mohammad. Killing the $GCH$ everywhere with a single real. J. Symbolic Logic 78 (2013), no. 3, 803--823. doi:10.2178/jsl.7803060.

Export citation