Categorical Abstract Algebraic Logic: Subdirect Representation of Pofunctors
نویسندگان
چکیده
منابع مشابه
Categorical Abstract Algebraic Logic: Subdirect Representation of Pofunctors
Pałasińska and Pigozzi developed a theory of partially ordered varieties and quasi-varieties of algebras with the goal of addressing issues pertaining to the theory of algebraizability of logics involving an abstract form of the connective of logical implication. Following their lead, the author has abstracted the theory to cover the case of algebraic systems, systems that replace algebras in t...
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Following work of Pa lasińska and Pigozzi on partially ordered varieties and quasi-varieties of universal algebras, the author recently introduced partially ordered systems (posystems) and partially ordered functors (pofunctors) to cover the case of the algebraic systems arising in categorical abstract algebraic logic. Analogs of the ordered homomorphism theorems of universal algebra were shown...
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The notion of subdirect irreducibility in the context of languages without equality, as presented by Elgueta, is extended in order to obtain subdirect representation theorems for abstract and reduced classes of structure systems. Structure systems serve as models of firstorder theories but, rather than having universal algebras as their algebraic reducts, they have algebraic systems in the sens...
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The theory of equivalential deductive systems, as introduced by Prucnal and Wroński and further developed by Czelakowski, is abstracted to cover the case of logical systems formalized as π-institutions. More precisely, the notion of an N-equivalence system for a given π-institution is introduced. A characterization theorem for N-equivalence systems, previously proven for N-parameterized equival...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2006
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870601042118