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 $T$ .

Title	Herbrand structure
Canonical name	HerbrandStructure
Date of creation	2013-03-22 14:33:13
Last modified on	2013-03-22 14:33:13
Owner	iwnbap (1760)
Last modified by	iwnbap (1760)
Numerical id	4
Author	iwnbap (1760)
Entry type	Definition
Classification	msc 03B10
Synonym	HerbrandModel HerbrandInterpretation
Related topic	HerbrandsTheoremFirstOrderLogic
Defines	HerbrandModel HerbrandInterpretation HerbrandUniverse