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arXiv · 2006.09572

Algebraic expansions of logics and algebras and a case study of Abelian l-groups and perfect MV-algebras

Miguel Campercholi·Diego Castaño·José Patricio Díaz Varela·Joan Gispert
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Abstract

An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \land p = q$. For a logic $L$ algebraized by a quasivariety $\mathcal{Q}$ we show that the AE-subclasses of $\mathcal{Q}$ correspond to certain natural expansions of $L$, which we call {\em algebraic expansions}. These turn out to be a special case of the expansions by implicit connectives studied by X. Caicedo. We proceed to characterize all the AE-subclasses of Abelian $\ell$-groups and perfect MV-algebras, thus fully describing the algebraic expansions of their associated logics.

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Miguel Campercholi, Diego Castaño, José Patricio Díaz Varela, Joan Gispert. 2020-06-17. Algebraic expansions of logics and algebras and a case study of Abelian l-groups and perfect MV-algebras. https://arxiv.org/abs/2006.09572

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