  We determine, up to the equivalence of first-order interdefinability, all
structures which are first-order definable in the random partial order. It
turns out that these structures fall into precisely five equivalence classes.
We achieve this result by showing that there exist exactly five closed
permutation groups which contain the automorphism group of the random partial
order, and thus expose all symmetries of this structure. Our classification
lines up with previous similar classifications, such as the structures
definable in the random graph or the order of the rationals; it also provides
further evidence for a conjecture due to Simon Thomas which states that the
number of structures definable in a homogeneous structure in a finite
relational language is, up to first-order interdefinability, always finite. The
method we employ is based on a Ramsey-theoretic analysis of functions acting on
the random partial order, which allows us to find patterns in such functions
and make them accessible to finite combinatorial arguments.
