Abstract

A union ultrafilter is an ultrafilter over the finite subsets of ω that has a base of sets of the form ${\text{FU}}\left$, where X is an infinite pairwise disjoint family and ${\text{FU}} = \left\{ {\bigcup {F|F} \in [X]^{ < \omega } \setminus \{ \emptyset \} } \right\}$. The existence of these ultrafilters is not provable from the $ZFC$ axioms, but is known to follow from the assumption that ${\text{cov}}\left = \mathfrak{c}$. In this article we obtain various models of $ZFC$ that satisfy the existence of union ultrafilters while at the same time ${\text{cov}}\left = \mathfrak{c}$.