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.
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 a subset of 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
[1][2]
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Theorems (list) & Paradoxes | |||||||||
Logics |
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Set theory |
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Syntax & Language |
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Proof theory | |||||||||
Model theory | |||||||||
Computability theory | |||||||||
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