Quasi-subtractive varieties

Journal of Symbolic Logic 76 (4):1261-1286 (2011)
  Copy   BIBTEX


Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras.algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety ������ the lattice of congruences of A is isomorphic to the lattice of deductive filters on A of the τ-assertional logic of ������. Moreover, if ������ has a constant 1 in its type and is 1-subtractive, the deductive filters on A ∈ ������ of the 1-assertional logic of ������ coincide with the ������-ideals of A in the sense of Gumm and Ursini, for which we have a manageable concept of ideal generation. However, there are isomorphism theorems, for example, in the theories of residuated lattices, pseudointerior algebras and quasi-MV algebras that cannot be subsumed by these general results. The aim of the present paper is to appropriately generalise the concepts of subtractivity and τ-regularity in such a way as to shed some light on the deep reason behind such theorems. The tools and concepts we develop hereby provide a common umbrella for the algebraic investigation of several families of logics, including substructural logics, modal logics, quantum logics, and logics of constructive mathematics



    Upload a copy of this work     Papers currently archived: 91,386

External links

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

Through your library

Similar books and articles

Quasi-varieties: A special access.Hans-Jürgen Hoehnke - 2004 - Studia Logica 78 (1-2):249 - 260.
Quasi-o-minimal structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
Quasi-truth in quasi-set theory.Otávio Bueno - 2000 - Synthese 125 (1-2):33-53.
Pretabular varieties of modal algebras.W. J. Blok - 1980 - Studia Logica 39 (2-3):101 - 124.
The subtractive : preface.Francois Wahl - 2008 - In Alain Badiou (ed.), Conditions. New York: Continuum.


Added to PP

49 (#318,154)

6 months
5 (#638,139)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Francesco Paoli
Universita di Cagliari
Tomasz Kowalski
La Trobe University

References found in this work

Equivalential logics.Janusz Czelakowski - 1981 - Studia Logica 40 (3):227-236.
Equivalential logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.
Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Topology and duality in modal logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.

View all 15 references / Add more references