Herbrand structure

For a languagePlanetmathPlanetmath , define the Herbrand universe to be the set of closed terms (alternatively ground terms) of L.

A structureMathworldPlanetmath 𝔐 for is a Herbrand structure if the domain of 𝔐 is the Herbrand universe of . This fixes the domain of 𝔐, and so each Herbrand structure can be identified with its interpretationMathworldPlanetmath, 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