Files

251264.pdf (371.37 KB)

Document type

Article

Version

Published version

Publication date

2023-03-01

All rights reserved

Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/225261

Algebraic expansions of logics

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

https://doi.org/10.1017/jsl.2022.47

Abstract

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.

Subject

Lògica algebraica, Estructures algebraiques ordenades, Teoria dels reticles

Subject (English)

Algebraic logic, Ordered algebraic structures, Lattice theory

Citation

Collections

Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CAMPERCHOLI, Miguel, et al. Algebraic expansions of logics. Journal of Symbolic Logic. 2023. Vol. 88, num. 1, pags. 74-92. ISSN 0022-4812. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/225261

Export metadata

JSON - METS

Share record