Convergence in MV-algebras

• Autores: George Georgescu, Fortuna Liguori, Giulia Martini
• Localización: Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology, ISSN-e 1134-5632, Vol. 4, Nº. 1, 1997, págs. 41-52
• Idioma: inglés
• Títulos paralelos:
  • Convergencia en álgebras MV
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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.