elementary diagram
{{Short description|Concept in model theory}}
{{for|diagrams of electrical circuits|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 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
References
- {{Citation | last1=Chang | first1=Chen Chung | last2=Keisler | first2=H. Jerome | author2-link=Howard Jerome Keisler | title=Model Theory | publisher=Elsevier | isbn=978-0-7204-0692-4 | year=1989}}
- {{Citation | last1=Hodges | first1=Wilfrid | author1-link=Wilfrid Hodges | title=A shorter model theory | publisher=Cambridge University Press | isbn=978-0-521-58713-6 | year=1997}}
- {{Citation | last1=Marker | first1=David | title=Model Theory: An Introduction | publisher=Springer-Verlag | location=Berlin, New York | series=Graduate Texts in Mathematics | isbn=978-0-387-98760-6 | year=2002}}
{{Mathematical logic}}
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