Journal of Symbolic Logic

A power function with a fixed finite gap everywhere

Carmi Merimovich

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

Abstract

We give an application of the extender based Radin forcing to cardinal arithmetic. Assuming $\kappa$ is a large enough cardinal we construct a model satisfying $2^{\kappa} = \kappa^{+n}$ together with $2^{\lambda} = \lambda^{+n}$ for each cardinal $\lambda < \kappa$, where $0 < n < \omega$. The cofinality of $\kappa$ can be set arbitrarily or $\kappa$ can remain inaccessible. When $\kappa$ remains an inaccessible, $V_{\kappa}$ is a model of ZFC satisfying $2^{\lambda} = \lambda^{+n}$ for all cardinals $\kappa$.

Article information

Source
J. Symbolic Logic, Volume 72, Issue 2 (2007), 361-417.

Dates
First available in Project Euclid: 30 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1185803615

Digital Object Identifier
doi:10.2178/jsl/1185803615

Mathematical Reviews number (MathSciNet)
MR2320282

Zentralblatt MATH identifier
1153.03036

Subjects
Primary: 03E35: Consistency and independence results 03E55: Large cardinals

Keywords
Forcing modified Radin forcing extender extender based forcing generalized continuum hypothesis singular cardinal hypothesis

Citation

Merimovich, Carmi. A power function with a fixed finite gap everywhere. J. Symbolic Logic 72 (2007), no. 2, 361--417. doi:10.2178/jsl/1185803615. https://projecteuclid.org/euclid.jsl/1185803615


Export citation