Stable ordered union ultrafilters and $\mathrm{cov}(\mathcal{M})<\mathfrak{c}$

Abstract

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

18 pages, final version