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.
be a first-order language and
For a model
to a new language by adding a new constant symbol
is a subset of the domain of
to the model The positive diagram of
, is the set of all those atomic sentences which hold in
while the negative diagram, denoted
thereof is the set of all those atomic sentences which do not hold in
The diagram
is the set of all atomic sentences and negations of atomic sentences of
[1][2] Symbolically,
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