Abstract
It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system F at, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction property of the intuitionistic propositional logic in which commuting conversions are not needed.
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Ferreira, F., Ferreira, G. The Faithfulness of Fat: A Proof-Theoretic Proof. Stud Logica 103, 1303–1311 (2015). https://doi.org/10.1007/s11225-015-9620-5
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DOI: https://doi.org/10.1007/s11225-015-9620-5