  The study of the global structure of ultrafilters on the natural numbers with
respect to the quasi-orders of Rudin-Keisler and Rudin-Blass reducibility was
initiated in the 1970s by Blass, Keisler, Kunen, and Rudin. In a 1973 paper
Blass studied the special class of P-points under the quasi-ordering of
Rudin-Keisler reducibility. He asked what partially ordered sets can be
embedded into the P-points when the P-points are equipped with this ordering.
This question is of most interest under some hypothesis that guarantees the
existence of many P-points, such as Martin's axiom for $\sigma$-centered
posets. In his 1973 paper he showed under this assumption that both
${\omega}_{1}$ and the reals can be embedded. This result was later repeated
for the coarser notion of Tukey reducibility. We prove in this paper that
Martin's axiom for $\sigma$-centered posets implies that every partial order of
size at most continuum can be embedded into the P-points both under
Rudin-Keisler and Tukey reducibility.
