## Journal of Symbolic Logic

### A power function with a fixed finite gap everywhere

Carmi Merimovich

#### 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

https://projecteuclid.org/euclid.jsl/1185803615

Digital Object Identifier
doi:10.2178/jsl/1185803615

Mathematical Reviews number (MathSciNet)
MR2320282

Zentralblatt MATH identifier
1153.03036

#### 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