## Journal of Symbolic Logic

### On the Cofinality of Ultrapowers

#### Abstract

We prove some restrictions on the possible cofinalities of ultrapowers of the natural numbers with respect to ultrafilters on the natural numbers. The restrictions involve three cardinal characteristics of the continuum, the splitting number $\mathfrak{s}$, the unsplitting number $\mathfrak{r}$, and the groupwise density number $\mathfrak{g}$. We also prove some related results for reduced powers with respect to filters other than ultrafilters.

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 2 (1999), 727-736.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745804

Mathematical Reviews number (MathSciNet)
MR1777781

Zentralblatt MATH identifier
0930.03060

JSTOR