Artículo
On the Equivalence Between MV-Algebras and l-Groups with Strong Unit
Fecha de publicación:
08/2015
Editorial:
Springer
Revista:
Studia Logica
ISSN:
0039-3215
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In “A new proof of the completeness of the Lukasiewicz axioms” (Trans Am Math Soc 88, 1959) Chang proved that any totally ordered MV-algebra A was isomorphic to the segment A≅Γ(A∗,u) of a totally ordered l-group with strong unit A*. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other (indexed by the integers). Moreover, he also show that any such group G can be recovered from its segment since G≅Γ(G,u)∗, establishing an equivalence of categories. In “Interpretation of AFC*-algebras in Lukasiewicz sentential calculus” (J Funct Anal 65, 1986) Mundici extended this result to arbitrary MV-algebras and l-groups with strong unit. He takes the representation of A as a sub-direct product of chains Ai, and observes that A↪∏iGi where Gi = Ai∗. Then he let A* be the l-subgroup generated by A inside ∏iGi. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang’s result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product l-group ∏iGi, avoiding entirely the notion of good sequence.
Palabras clave:
MV ALGEBRAS
,
L GROUPS
,
GOOD SEQUENCES
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Dubuc, Eduardo Julio; Poveda, Y. A.; On the Equivalence Between MV-Algebras and l-Groups with Strong Unit; Springer; Studia Logica; 103; 4; 8-2015; 807-814
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