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Herbrand structure

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Title: Herbrand structure  
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Subject: Mathematical logic, Inductive logic programming, List of mathematical logic topics
Collection: Mathematical Logic
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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.

See also

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

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