Herbrand structure

In mathematics, for a language $\mathcal{L}$ , define the Herbrand universe to be the set of ground terms of $\mathcal{L}$ .

A structure $\mathfrak{M}$ for $\mathcal{L}$ is a Herbrand structure if the domain of $\mathfrak{M}$ is the Herbrand universe of $\mathcal{L}$ and the interpretation of $\mathfrak{M}$ is a Herbrand interpretation. This fixes the domain of $\mathfrak{M}$ , and so each Herbrand structure can be identified with its interpretation.

A Herbrand model of a theory $T$ is a Herbrand structure that is a model of $T.$

Herbrand structure

See also