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Completeness Theorems via the Double Dual Functor |
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| Authors: | Galli Adriana Sagastume Marta Reyes Gonzalo E. |
| Affiliation: | (1) Universidad de La Plata, Canada;(2) Université de Montréal, Canada |
| Abstract: | The aim of this paper is to apply properties of the double dual endofunctor on the category of bounded distributive lattices and some extensions thereof to obtain completeness of certain non-classical propositional logics in a unified way. In particular, we obtain completeness theorems for Moisil calculus, n-valued Łukasiewicz calculus and Nelson calculus. Furthermore we show some conservativeness results by these methods. This revised version was published online in June 2006 with corrections to the Cover Date. |
| Keywords: | category of distributive lattices double dual functor non-classical propositional logics (intuitionistic, bi-intuitionistic, Moisil, Ł ukasiewicz, Nelson) completeness theorems conservative extensions |
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