Categorical abstract algebraic logic: Ordered equational logic and algebraizable povarieties
type: Item
instance of: scholarly article
title: Categorical abstract algebraic logic: Ordered equational logic and algebraizable povarieties
zbMATH Open document ID: 1117.03072
author: George Voutsadakis
published in: Order
publication date: 2007-04-26T00:00:00Z
review text: This paper contains the fourth (and final) installment on research concerning an extension of some of the results on partially ordered varieties and quasi-varieties of partially ordered universal algebras obtained by Palasińska and Pigozzi in the context of abstract algebraic logic and reported in \textit{D. Pigozzi}'s lecture notes available at \url{http://www.math.iastate.edu/dpigozzi}. A syntactic apparatus is introduced for the study of the algebraic properties of classes of partially ordered algebraic systems (a.k.a. partially ordered functors (pofunctors)). A Birkhoff-style order HSP theorem and a Mal'tsev-style order SLP theorem are proved for partially ordered varieties and partially ordered quasivarieties, respectively, of partially ordered algebraic systems based on this syntactic apparatus. Finally, the notion of a finitely algebraizable partially-ordered quasivariety, in the spirit of Palasińska and Pigozzi, is introduced and some of the properties of these quasi-povarieties are explored in the categorical framework.
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 08C05
zbMATH DE Number: 5146175
zbMATH Keywords: polarities
zbMATH Keywords: reduced products
zbMATH Keywords: subdirect products
zbMATH Keywords: closure operators
zbMATH Keywords: \(\pi\)-institutions
zbMATH Keywords: protoalgebraic logics
zbMATH Keywords: algebraizable logic
zbMATH Keywords: partially ordered functors
zbMATH Keywords: partially ordered quasivarieties
zbMATH Keywords: partially ordered algebraic systems
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: s11083-006-9048-7
OpenAlex ID: W2070256301
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DOI: 10.1007/S11083-006-9048-7
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description: scientific article; zbMATH DE number 5146175