Duality for lattice-ordered algebras and for normal algebraizable logics

Studia Logica 58 (3):403-450 (1997)
  Copy   BIBTEX

Abstract

Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality.In part II, we consider lattice-ordered algebras (lattices with additional operators), extending the Jónsson and Tarski representation results [30] for Boolean algebras with Operators. Our work can be seen as developing, and indeed completing, Dunn's project of gaggle theory [13, 14]. We consider general lattices (rather than Boolean algebras), with a broad class of operators, which we dubb normal, and which includes the Jónsson-Tarski additive operators. Representation of l-algebras is extended to full duality.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,100

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
65 (#250,245)

6 months
8 (#365,731)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1973 - In Hugues Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam and London: North-Holland Publishing Company. pp. 199-243.
Logics without the contraction rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.

View all 18 references / Add more references