Diagram (mathematical logic)
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.Definition
Let be a first-order language and be a theory over. For a model of one expands to a new language
by adding a new constant symbol for each element in, where is the domain of. Now one may expand to the model
The diagram of is the set of all atomic sentences and negations of atomic sentences of that hold in.
