Representation theory of MV-algebras

DUBUC, EDUARDO J.; POVEDA, YURI

ANNALS OF PURE AND APPLIED LOGIC

ELSEVIER SCIENCE BV

Año: 2010 vol. 161 p. 1024 - 1046

0168-0072

In this paper we develop a general representation theory forMV-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 globalsections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of a sheaf ofMV-chains on a compact topological space. This result is intimatelyrelated to McNaughton´s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton´s. 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.