Elementary diagram

For diagrams of electrical circuits, see Circuit diagram.

In the mathematical field of model theory, the elementary diagram of a structure is the set 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 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).

References

Chang, Chen Chung; Keisler, H. Jerome (1989), Model Theory, Elsevier, ISBN 978-0-7204-0692-4
Hodges, Wilfrid (1997), A shorter model theory, Cambridge University Press, ISBN 978-0-521-58713-6
Marker, David (2002), Model Theory: An Introduction, Graduate Texts in Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98760-6

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