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).
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References
Cignoli R., D’Ottaviano I., Mundici D.: Algebraic foundations of many-valued reasoning, in Trends in Logic, Vol. 7.. Kluwer, Dordrecht (2000)
Ferraioli A.R., Lettieri A.: Representations of MV-algebras by sheaves. Mathematical Logic Quarterly 1, 27–43 (2011)
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Presented by Daniele Mundici
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Dubuc, E.J., Poveda, Y. The Intimate Relationship Between the McNaughton and the Chinese Remainder Theorems for MV-algebras. Stud Logica 101, 483–485 (2013). https://doi.org/10.1007/s11225-011-9368-5
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DOI: https://doi.org/10.1007/s11225-011-9368-5