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 $\mathcal{L}.$ This fixes the domain of $\mathfrak{M}$, and so each Herbrand structure can be identified with its interpretation, leading to the alternative nomenclature of Herbrand interpretation.

A Herbrand model of a theory T is a Herbrand structure which is a model of T.

See also

• Herbrand base
• Herbrand's theorem

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This article incorporates material from Herbrand structure on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

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