Studia Logica

, Volume 101, Issue 3, pp 483–485

The Intimate Relationship Between the McNaughton and the Chinese Remainder Theorems for MV-algebras

Article

Abstract

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli and Lettieri (Math Logic Q 1:27–43, 2011).

Keywords

MV-algebras McNaughton Theorem Chinese Theorem 

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References

  1. 1.
    Cignoli R., D’Ottaviano I., Mundici D.: Algebraic foundations of many-valued reasoning, in Trends in Logic, Vol. 7.. Kluwer, Dordrecht (2000)CrossRefGoogle Scholar
  2. 2.
    Ferraioli A.R., Lettieri A.: Representations of MV-algebras by sheaves. Mathematical Logic Quarterly 1, 27–43 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dpto, de Matematicas, F.C.E y N.Universidad de Buenos Aires CABABuenos AiresArgentina
  2. 2.Dpto. de MatematicasUniversidad Tecnologica de PereiraPereiraColombia

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