Duality for lattice-ordered algebras and for normal algebraizable logics
type: Item
instance of: scholarly article
title: Duality for lattice-ordered algebras and for normal algebraizable logics
zbMATH Open document ID: 0886.06002
DOI: 10.1023/A:1004982417404
author: Chrysafis Hartonas
published in: Studia Logica
publication date: 1998-05-10T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 03G99
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 1071489
zbMATH Keywords: algebraic semantics
zbMATH Keywords: topological representation
zbMATH Keywords: duality
zbMATH Keywords: lattice-ordered algebras
zbMATH Keywords: canonical frames
zbMATH Keywords: Kripke-style semantics
reviewed by: Manuel Abad
MaRDI profile type: Publication
full work available at URL: a:1004982417404
OpenAlex ID: W1519705629
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description: scientific article; zbMATH DE number 1071489