Let ${\displaystyle {\mathcal {L}}}$  be a first-order language and ${\displaystyle T}$  be a theory over ${\displaystyle {\mathcal {L}}.}$  For a model ${\displaystyle {\mathfrak {A}}}$  of ${\displaystyle T}$  one expands ${\displaystyle {\mathcal {L}}}$  to a new language

${\displaystyle {\mathcal {L}}_{A}:={\mathcal {L}}\cup \{c_{a}:a\in A\}}$ 

by adding a new constant symbol ${\displaystyle c_{a}}$  for each element ${\displaystyle a}$  in ${\displaystyle A,}$  where ${\displaystyle A}$  is a subset of the domain of ${\displaystyle {\mathfrak {A}}.}$  Now one may expand ${\displaystyle {\mathfrak {A}}}$  to the model

${\displaystyle {\mathfrak {A}}_{A}:=({\mathfrak {A}},a)_{a\in A}.}$ 

The positive diagram of ${\displaystyle {\mathfrak {A}}}$ , sometimes denoted ${\displaystyle D^{+}({\mathfrak {A}})}$ , is the set of all those atomic sentences which hold in ${\displaystyle {\mathfrak {A}}}$  while the negative diagram, denoted ${\displaystyle D^{-}({\mathfrak {A}}),}$  thereof is the set of all those atomic sentences which do not hold in ${\displaystyle {\mathfrak {A}}}$ .

The diagram ${\displaystyle D({\mathfrak {A}})}$  of ${\displaystyle {\mathfrak {A}}}$  is the set of all atomic sentences and negations of atomic sentences of ${\displaystyle {\mathcal {L}}_{A}}$  that hold in ${\displaystyle {\mathfrak {A}}_{A}.}$ ^[1][2] Symbolically, ${\displaystyle D({\mathfrak {A}})=D^{+}({\mathfrak {A}})\cup \neg D^{-}({\mathfrak {A}})}$ .

• Elementary diagram