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Studying relationships between recursion theory and categorical theory, can find properties of the recursive universe that can be represented by universal properties. It is possible to generalize in some respects this universe to search examples of recursive properties that are not from the arithmetical universe and well understood from other perspectives, the Gödel's incompleteness theorem. [ABSTRACT FROM AUTHOR]

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. [Copyright &y& Elsevier]