A topological duality for tense $\boldsymbol{LM_n}$-algebras and applications1
Aldo Victorio Figallo, Inés Pascual, Gustavo Pelaitay · Logic Journal of IGPL · 2018
In 2007, tense |$n$|-valued Łukasiewicz–Moisil algebras (or tense |$LM_n$|-algebras) were introduced by Diaconescu and Georgescu as an algebraic counterpart of the tense |$n$|-valued Moisil logic. In this article we continue the study of tense |$LM_n$|-algebras initiated by Figallo and Pelaitay (2014, Log. J. IGPL, 22, 255–267). More precisely, we determine a topological duality for these algebras. This duality enables us not only to describe the tense |$LM_n$|-congruences on a tense |$LM_n$|-algebra, but also to characterize the simple and subdirectly irreducible tense |$LM_n$|-algebras. Furthermore, by means of the aforementioned duality, a representation theorem for tense |$LM_n$|-algebras is proved, which was formulated and proved by a different method by Georgescu and Diaconescu (2007, Fund. Inform., 81, 379–408).