Generic automorphisms of the universal partial order

Abstract

We show that the countable universal-homogeneous partial order $(P,<)$ has a generic automorphism as defined by the second author, namely that it lies in a comeagre conjugacy class of Aut$(P,<)$. For this purpose, we work with ‘determined’ partial finite automorphisms that need not be automorphisms of finite substructures (as in the proofs of similar results for other countable homogeneous structures) but are nevertheless sufficient to characterize the isomorphism type of the union of their orbits.