Elementary diagram

In the mathematical field of model theory, the elementary diagram of a structure is the set of all sentences with parameters from the structure that are true in the structure. It is also called the complete diagram. In the mathematical field of model theory, the elementary diagram of a structure is the set of all sentences with parameters from the structure that are true in the structure. It is also called the complete diagram. Let M be a structure in a first-order language L. An extended language L(M) is obtained by adding to L a constant symbol ca for every element a of M. The structure M can be viewed as an L(M) structure in which the symbols in L are interpreted as before, and each new constant ca is interpreted as the element a. The elementary diagram of M is the set of all L(M) sentences that are true in M (Marker 2002:44).