On the existential interpretability of structures

We introduce and study the notion of $\exists$-interpretability of constructive algebraic structures. It is shown that any finite partially ordered set is embeddable into the semilattice this interpretability generates; we also prove the existence of universal computable structures. As an application of this concept, we consider the transformations of abstract databases and their queries in case when one data structure is $\exists$-interpretable in another one.