Duality for lattice-ordered algebras and for normal algebraizable logics (Q1368914)

This paper consists of three parts. In Part I, a new topological representation for general lattices is presented, and this representation is extended to a full duality. In Part II, the Jónsson and Tarski representation results for Boolean algebras with operators are extended for lattice-ordered algebras (lattices with additional operators). Finally, in Part III, some applications in logic are discussed. The representation results are used to construct canonical frames for certain logical systems and to obtain a duality for their algebraic and Kripke-style semantics.