A non-principal ultrafilter $\mathcal{U}$ on $\omega$ is a **p-point** (or **weakly selective**) iff for every partition $\omega = \bigsqcup _{n < \omega} Z_n$ into null sets, i.e each $Z_n \not \in \mathcal{U}$, there exists a measure one set $S \in \mathcal{U}$ such that $S \cap Z_n$ is finite for each $n$.

A non-principal ultrafilter $\mathcal{U}$ on $\omega$ is **Ramsey** (or **selective**) iff for every partition as above, there exists a measure one set $S$ such that $|S \cap Z_n| = 1$ for each $n$.

**Clearly, every Ramsey ultrafilter is a p-point. What is known about the converse?**

I couldn't find anything, not even a consistency result, in any searches I've done or sources I've checked. Is very little known/published about the converse?