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arXiv · 2106.07707

An alternative axiomatic presentation of Nelson algebras

Juan Manuel Cornejo·Andrés Gallardo·Luiz Monteiro·Ignacio Viglizzo
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Abstract

Nelson algebras are defined in [Diana Brignole and Ant\'onio Monteiro. Caract\'erisation des alg\`ebres de Nelson par des \'egalit\'es. {I}, {II}. Proc. Japan Acad., 43:279--283; 284--285, 1967.] in terms of the language $\langle \land,\lor,\to,\sim,1\rangle$. In 1962, Diana Brignole [Diana Brignole. Axiomatizaci\'on de un $N$-reticulado. Revista de la Uni\'on Matem\'atica Argentina, XXI(3):147--148, 1965.], solved the problem proposed by Antonio Monteiro, of giving an axiomatization of Nelson algebras in terms of the connectives $\rightarrowtail$, $\land$ and the constant $0=\sim 1$. In this work, we present for the first time a complete proof of this fact, and also show the dependence and independence of some of the axioms proposed by Brignole.

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Juan Manuel Cornejo, Andrés Gallardo, Luiz Monteiro, Ignacio Viglizzo. 2021-06-14. An alternative axiomatic presentation of Nelson algebras. https://arxiv.org/abs/2106.07707

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