We show the consistency of the statement: "the set of regular cardinals which are the characters of ultrafilters on ω is not convex". We also deal with the set of π-characters of ultrafilters on ω.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-2-5, author = {Saharon Shelah}, title = {The spectrum of characters of ultrafilters on $\omega$}, journal = {Colloquium Mathematicae}, volume = {111}, year = {2008}, pages = {213-220}, zbl = {1142.03028}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-2-5} }
Saharon Shelah. The spectrum of characters of ultrafilters on ω. Colloquium Mathematicae, Tome 111 (2008) pp. 213-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-2-5/