Two applications of Boolean models

Archive for Mathematical Logic 37 (3):143-147 (1998)
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Semantical arguments, based on the completeness theorem for first-order logic, give elegant proofs of purely syntactical results. For instance, for proving a conservativity theorem between two theories, one shows instead that any model of one theory can be extended to a model of the other theory. This method of proof, because of its use of the completeness theorem, is a priori not valid constructively. We show here how to give similar arguments, valid constructively, by using Boolean models. These models are a slight variation of ordinary first-order models, where truth values are now regular ideals of a given Boolean algebra. Two examples are presented: a simple conservativity result and Herbrand's theorem



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Saturated models of universal theories.Jeremy Avigad - 2002 - Annals of Pure and Applied Logic 118 (3):219-234.
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