Abstract
A polyhedron in Rn is a finite union of simplexes in Rn. An MV-algebra is polyhedral if it is isomorphic to the MV-algebra of all continuous [0,1]-valued piecewise linear functions with integer coefficients, defined on some polyhedron P in Rn. We characterize polyhedral MV-algebras as finitely generated subalgebras of semisimple tensor products S⊗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 Z-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.
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