Polyhedral MV-algebras

A polyhedron   in RnRn is a finite union of simplexes in RnRn. An MV-algebra is polyhedral   if it is isomorphic to the MV-algebra of all continuous [0,1][0,1]-valued piecewise linear functions with integer coefficients, defined on some polyhedron P   in RnRn. We characterize polyhedral MV-algebras as finitely generated subalgebras of semisimple tensor products S⊗FS⊗F with S simple and F   finitely presented. We establish a duality between the category of polyhedral MV-algebras and the category of polyhedra with ZZ-maps. We prove that polyhedral MV-algebras are preserved under various kinds of operations, and have the amalgamation property. Strengthening the Hay–Wójcicki theorem, we prove that every polyhedral MV-algebra is strongly semisimple, in the sense of Dubuc–Poveda.