In this paper we introduce two kinds of unary operations on abelian ℓ-groups with a positive distinguished element u. One of them, called demiquantifier of type I, behaves like an existential quantifier (in the sense of Cimadamore and Varela) in the negative cone, and like a universal quantifier in the positive cone. The other kind of unary operation we introduce, called demiquantifier of type II, satisfies analogous properties to demiquantifiers of type I via a translation of the negative cone, by means of the element u. These unary operations are interdefinable with the usual existential quantifiers, provided the distinguished element u is a strong unit. Moreover, if G is an abelian ℓ-group, then the restriction of a demiquantifier of type II to the MV-algebra Γ (G, u) yields a different type of quantifier, where Γ is Mundici’s functor. These quantifiers are interdefinable with the usual existential quantifiers on MV-algebras given by Rutledge, provided that the involution of the corresponding MV-algebras have a fixed point. © 2018, Springer Nature Switzerland AG.
Documento: | Artículo |
Título: | Demiquantifiers on ℓ -groups |
Autor: | Petrovich, A. |
Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Uruguay 151, Santa Rosa, La Pampa, Argentina |
Palabras clave: | MV-algebras; Quantifiers; ℓ-groups |
Año: | 2018 |
Volumen: | 79 |
Número: | 3 |
DOI: | http://dx.doi.org/10.1007/s00012-018-0552-6 |
Título revista: | Algebra Universalis |
Título revista abreviado: | Algebra Univers. |
ISSN: | 00025240 |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00025240_v79_n3_p_Petrovich |