An alternative axiomatic presentation of Nelson algebras

CORNEJO, JUAN MANUEL; ANDRÉS GALLARDO; MONTEIRO, LUIZ F.; VIGLIZZO, IGNACIO D.

Actas del Congreso Antonio Monteiro

Congreso Dr. Antonio A. R. Monteiro

Lugar: Bahía Blanca; Año: 2023 vol. 2021 p. 129 - 147

0327-9170

Nelson algebras are defined in cite{brignole67caracterisation} in terms of the language $langle land,lor,o,sim,1angle$.In 1962, Diana Brignole cite{Brignole65Nlattice}, solved the problem proposed by Antonio Monteiro, of giving an axiomatization of Nelson algebras in terms of the connectives $oo$, $land$ 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.