Elementary Diagrams in Institutions

We generalize the method of diagrams from conventional model theory to a simple institution-independent (i.e. independent of the details of the actual logic formalized as an institution) framework based on a novel categorical concept of elementary diagram of a model. We illustrate the power of our institution-independent method of elementary diagrams by developing several applications to institution liberality, institution-independent quasi-varieties, and limits and colimits of presentation models. The results obtained are illustrated systematically with examples from several different specification logics. In the introduction we also discuss the relevance of our institution-independent approach to the model theory of algebraic specification and computing science, but also to conventional and abstract model theory.