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Categorical Abstract Algebraic Logic: Ordered Equational Logic and Algebraizable PoVarieties

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Abstract

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’cev-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 quasi-variety, in the spirit of Pałasińska and Pigozzi, is introduced and some of the properties of these quasi-povarieties are explored in the categorical framework.

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  1. School of Mathematics and Computer Science, Lake Superior State University, 650 W. Easterday Avenue, Sault Sainte Marie, MI, 49783, USA

    George Voutsadakis

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  1. George Voutsadakis
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Correspondence to George Voutsadakis.

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Voutsadakis, G. Categorical Abstract Algebraic Logic: Ordered Equational Logic and Algebraizable PoVarieties. Order 23, 297–319 (2006). https://doi.org/10.1007/s11083-006-9048-7

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