MV-algebras were introduced in 1958 by Chang [4] and they are models of Lukasiewicz infinite-valued logic. Chang gives a correspondence between the category of linearly ordered MV-algebras and the category of linearly ordered abelian l-groups.
Mundici [10] extended this result showing a categorical equivalence between the category of the MV-algebras and the category of the abelian l-groups with strong unit.
In this paper, starting from some definitions and results in abelian l-groups, we shall study the convergent sequences and the Cauchy sequences in an MV-algebra.
The main result is the construction of the Cauchy completion A* of an MV-algebra A.
It is proved that a complete MV-algebra is also Cauchy complete. Additional results on atomic and complete MV-algebras are also given.
@article{urn:eudml:doc:39099,
title = {Convergence in MV-algebras.},
journal = {Mathware and Soft Computing},
volume = {4},
year = {1997},
pages = {41-52},
zbl = {0939.06010},
mrnumber = {MR1463107},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39099}
}
Georgescu, George; Liguori, Fortuna; Martini, Giulia. Convergence in MV-algebras.. Mathware and Soft Computing, Tome 4 (1997) pp. 41-52. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39099/