Finite axiomatizations for existentially closed posets and semilattices
It is well known that any universal first order relational theory K with the joint embedding and the amalgamation property admits an \(\aleph_ 0\)-categorical model-completion \(\bar K\) which is given by formalizing the finite diagrams of models of K according to the back and forth method [e.g. the reviewer's dissertation, Z. Math. Logik Grundlagen Math. 15, 37-48 (1969; Zbl 0188.321), p. 42, footnote]. Applied to totally ordered sets the method yields the densely ordered sets without endpoints. The authors establish similar finite axiomatizations of \(\bar K\) for posets and semilattices.
scientific article; zbMATH DE number 3987258