Diagram of a structure

The diagram of $M$ is the set of atomic and negated atomic sentences true in the expansion by constants naming every element of $M$. Its elementary diagram contains every sentence true in that expansion. Models of these diagrams correspond respectively to embeddings and elementary embeddings of $M$.

The method of diagrams adds the diagram or elementary diagram of a structure to a theory and applies compactness. A resulting model supplies an embedding or elementary embedding of the named structure.