Generic automorphisms of the universal partial order (Q2718953)

An isomorphism between substructures of a relational structure is called a partial automorphism. If \(p\) and \(q\) are partial automorphisms, then \(q\) is an extension of \(p\) if \(p\) is a restriction of \(q\) to a smaller domain. Let \(P\) be the set of all partial automorphisms. Then \(A\subseteq P\) is called cofinal if every member of \(P\) has an extension in \(A\). The authors prove that there is a cofinal subset of the set of all finite partial automorphisms of \((\mathbb{Q},<)\) having the amalgamation property. Next they consider \((P,<)\), the countable universal-homogeneous partial order, and prove that the family of its ``determined'' partial automorphisms has the amalgamation property. I skip the definition of ``determinacy''. It follows that \((P,<)\) possesses a generic automorphism in the sense of \textit{J. K. Truss} [Proc. Lond. Math. Soc., III. Ser. 65, 121-141 (1992; Zbl 0723.20001)].