Herbrand structure

For a language $\\mathcal{L}$ , define the Herbrand universe to be the set of closed terms (alternatively ground terms) of $L$ .

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 $T$ .

单词	HerbrandStructure
释义	Herbrand structure For a language $\\mathcal{L}$ , define the Herbrand universe to be the set of closed terms (alternatively ground terms) of $L$ . 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 $T$ .
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