In the
mathematical field of
model theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...
, 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 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
In mathematics and other formal sciences, first-order or first order most often means either:
* "linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of high ...
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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