Dualidades: de Birkhoff à N4-reticulados limitados

Abstract

The present study aims to introduce the Birkhoff duality, extending for Stone duality and followed by Priestley duality, as well as the basic concepts for understanding them. It will then be introduced a positive modal operator and shown that Priestley duality applies for Priestley spaces with a certain type of relation. After that, it will be done a duality among bounded N4 and NE-Sp, using the equivalence between bounded N4 and bounded TWIST as a shortcut. In addition to presenting some ideas about non-involutive bilattices in the appendix.