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Finite basis theorem for Filter-distributive protoalgebraic deductive systems and strict universal horn classes
Studia Logica 74 (1-2):233 - 273 (2003)
Abstract
We show that a finitely generated protoalgebraic strict universal Horn class that is filter-distributive is finitely based. Equivalently, every protoalgebraic and filter-distributive multidimensional deductive system determined by a finite set of finite matrices can be presented by finitely many axioms and rules.Other Versions
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Citations of this work
Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.
Order algebraizable logics.James G. Raftery - 2013 - Annals of Pure and Applied Logic 164 (3):251-283.
The Beth Property in Algebraic Logic.W. J. Blok & Eva Hoogland - 2006 - Studia Logica 83 (1-3):49-90.
Quasivarieties with Definable Relative Principal Subcongruences.Anvar M. Nurakunov & M. M. Stronkowski - 2009 - Studia Logica 92 (1):109-120.
References found in this work
An algebraic characterization of the notion of structural completeness.Tadeusz Prucnal & Andrzej Wronski - 1974 - Bulletin of the Section of Logic 3 (1):30-33.
Some theorems on structural consequence operations.Stephen L. Bloom - 1975 - Studia Logica 34 (1):1 - 9.
On distributivity of closure systems.Wojciech Dzik & Roman Suszko - 1977 - Bulletin of the Section of Logic 6 (2):64-66.
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