On the Cofinality of Ultrapowers

Blass, Andreas; Mildenberger, Heike

J. Symbolic Logic, Tome 64 (1999) no. 1, p. 727-736 / Harvested from Project Euclid

Résumé

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.

Publié le : 1999-06-14
Classification:

@article{1183745804,
     author = {Blass, Andreas and Mildenberger, Heike},
     title = {On the Cofinality of Ultrapowers},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 727-736},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745804}
}

Blass, Andreas; Mildenberger, Heike. On the Cofinality of Ultrapowers. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  727-736. http://gdmltest.u-ga.fr/item/1183745804/