aleph_0-categorical Structures: Endomorphisms and Interpretations

We extend the Ahlbrandt–Ziegler analysis of interpretability in aleph_0-categorical structures by showing that existential interpretation is controlled by the monoid of self–embeddings and positive existential interpretation of structures without constant endomorphisms is controlled by the monoid of endomorphisms in the same way as general interpretability is controlled by the automorphism group.