Let $\mathfrak{u}$ denote the ultrafilter number, which is defined to be the minimum cardinality of a subset of $\mathcal{P}(\mathbb N)$ which is a base for a nonprincipal ultrafilter on $\mathbb{N}$. Clearly $\aleph_1\leq \frak{u}\leq 2^{\aleph_0}$, so it is only interesting to study $\frak{u}$ under the negation of CH. Kunen proved that it is consistent that CH fails and that $\frak{u}=\aleph_1$. Martin's axiom implies that $\frak{u}=2^{\aleph_0}$.

Is it consistent that $\aleph_1<\frak{u}<2^{\aleph_0}$? If so, can I please have a reference?