We present an equivalence between the category of Nelson Paraconsistent lattices (NPc-lattices) and a category of pairs of Brouwerian algebras and regular filters. Specializing such category of pairs to Gödel hoops, we get the subvariety of Gödel NPc-lattices and, using the dual equivalence of finite Gödel hoops with finite trees, we obtain a duality for finite Gödel NPc-lattices. This duality is used to describe finitely generated free Gödel NPc-lattices.
On the category of Nelson paraconsistent lattices
GERLA, BRUNELLA;
2017-01-01
Abstract
We present an equivalence between the category of Nelson Paraconsistent lattices (NPc-lattices) and a category of pairs of Brouwerian algebras and regular filters. Specializing such category of pairs to Gödel hoops, we get the subvariety of Gödel NPc-lattices and, using the dual equivalence of finite Gödel hoops with finite trees, we obtain a duality for finite Gödel NPc-lattices. This duality is used to describe finitely generated free Gödel NPc-lattices.
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