most recent 30 from http://mathoverflow.net 2013-05-23T02:27:03Z http://mathoverflow.net/feeds/question/76495 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/76495/existence-of-non-principal-ultrafilters-on-sets Stefan Geschke 2011-09-27T11:22:46Z 2011-09-27T11:55:08Z

<p>Is it known to be consistent with ZF that there is no non-principal ultrafilter on any infinite set? (Feel free to use your favorite interpretation of "infinite" in this context. If infinite just meant infinite ordinals, that would be fine, too. You may use all kinds of large cardinals.)</p>

http://mathoverflow.net/questions/76495/existence-of-non-principal-ultrafilters-on-sets/76499#76499 François G. Dorais 2011-09-27T11:55:08Z 2011-09-27T11:55:08Z

<p>Yes, it is consistent with ZF that every ultrafilter is principal. This is a result of Andreas Blass, <em>A model without ultrafilters</em>, Bull. Acad. Polon. Sci. 25 (1977), 329&ndash;331.</p>