The only examples of ultranets/ultrafilters described in Bourbaki and Willard are the trivial ones (generated by a single point). I know that their existence relies in general on the axiom of choice or the ultrafilter lemma.


I have two questions:


has any non-trivial ultranet been constructed?


if not:


is there any strong reason why no non-trivial ultranet has/will ever be constructed?



How to make an ultranet
It is not possible to prove in ZF alone that there is a nonprincipal ultrafilter. This was established by Andreas Blass in 1977. [*A model without ultrafilters*, 
Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 329–331, [MR0476510](http://www.ams.org/mathscinet-getitem?mr=476510)]


