Hakim duality for mv-algebras

DUBUC, EDUARDO J.

Montreal, Canada.

Conferencia; CATEGORY THEORY RESEARCH CENTER SEMINAR; 2008

McGill University

We develop the basic duality theory for mv-algebras along the lines of Hakim work on rings (as in R. Hartshorne, "Algebraic Geometry", Springer 1977), and as a particular case of the general categorical theory (as in M. Coste, "Localization, Spectra and Sheaf Representation", Springer LNM 753). We can represent anymv-algebra as the global sections of a sheaf of mv-chains. The realinterval [0,,1] is a mv-algebra, and an application of our results is the McNaughton theorem that says that any piecewise linear [0,1]-valued function on [0, 1]^n  is globally given by a n-ary term of the theory. We shall not assume any knowledge on mv-algebras, and all the mv-algebra theory we shall need can be rapidly explained.