Abstract.
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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Received December 5, 1995
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Coquand, T. Two applications of Boolean models. Arch Math Logic 37, 143–147 (1998). https://doi.org/10.1007/s001530050088
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DOI: https://doi.org/10.1007/s001530050088