In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.

Definition

Let be a first-order language and be a theory over For a model of one expands to a new language

by adding a new constant symbol for each element in where is the domain of Now one may expand to the model

The diagram of is the set of all atomic sentences and negations of atomic sentences of that hold in [1][2]

See also

References

  1. ^ Hodges, Wilfrid (1993). Model theory. Cambridge University Press. ISBN 9780521304429.
  2. ^ Chang, C. C.; Keisler, H. Jerome (2012). Model Theory (Third ed.). Dover Publications. pp. 672 pages.