Diagram (mathematical logic)

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]

References

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