In the
mathematical
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
field of
model theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...
, the elementary diagram of a
structure
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
is the
set
Set, The Set, SET or SETS may refer to:
Science, technology, and mathematics Mathematics
*Set (mathematics), a collection of elements
*Category of sets, the category whose objects and morphisms are sets and total functions, respectively
Electro ...
of all
sentences
The ''Sentences'' (. ) is a compendium of Christian theology written by Peter Lombard around 1150. It was the most important religious textbook of the Middle Ages.
Background
The sentence genre emerged from works like Prosper of Aquitaine's ...
with parameters from the structure that are true in the structure. It is also called the complete diagram.
Definition
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 ''c''
''a'' 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 ''c''
''a'' 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).
See also
*
Diagram (model theory)
References
*
*
*
Model theory
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