Algebraic expansions of logics
An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists!\wedge p=q$. For a logic $L$ algebraized by a quasivariety $\mathcal{Q}$ we show that the AEsubclasses of $\mathcal{Q}$ correspond to certain natural expansions of $L$, w...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/225261 |
| Acceso en línea: | https://hdl.handle.net/2445/225261 |
| Access Level: | acceso abierto |
| Palabra clave: | Lògica algebraica Estructures algebraiques ordenades Teoria dels reticles Algebraic logic Ordered algebraic structures Lattice theory |
| Sumario: | An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists!\wedge p=q$. For a logic $L$ algebraized by a quasivariety $\mathcal{Q}$ we show that the AEsubclasses of $\mathcal{Q}$ correspond to certain natural expansions of $L$, which we call algebraic expansions. These turn out to be a special case of the expansions by implicit connectives studied by $\mathbf{X}$. 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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