Free Interpretation, Quotient Interpretation and Substitution of a Letter with a Term for First Order Languages
Marco Caminati (2011)
Formalized Mathematics
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Fourth of a series of articles laying down the bases for classical first order model theory. This paper supplies a toolkit of constructions to work with languages and interpretations, and results relating them. The free interpretation of a language, having as a universe the set of terms of the language itself, is defined.The quotient of an interpreteation with respect to an equivalence relation is built, and shown to remain an interpretation when the relation respects it. Both the concepts...