Elementary 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
[edit]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 ca 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 ca 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
[edit]References
[edit]- 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
| General | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Theorems (list) and paradoxes | |||||||||
| Logics |
| ||||||||
| Set theory |
| ||||||||
| Formal systems (list), language and syntax |
| ||||||||
| Proof theory | |||||||||
| Model theory | |||||||||
| Computability theory | |||||||||
| Related | |||||||||
 | This mathematical logic-related article is a stub. You can help Wikipedia by expanding it. |