Finitely presented MV-algebras, unital lattice ordered abelian groups and rational polyhedra - together
Daniele Mundici · 2014
nite string of symbols representing a triangulated rational polyhedron PM , and homeomorphism is understood as (rational) PL-homeomorphism. Viewing the recognizability problem from the viewpoint of algorithmic complexity theory, one may naturally take into account the amount of information needed to specify PM . We are thus left with the category of rational polyhedra (objects) with integer PL-maps (arrows). A new geometry arises, where the ane group over the integers takes on the same role as the isometry group does in euclidean geometry. Many arithmetic geometric computable invariants emerge in this new category, which make no sense for rational polyhedra with rational PL-maps. We discuss in particular the rational measure of rational polyhedra. Its role and applicability is amplied by their duality with nitely presented MV-algebras, the algebras of nitely axiomatizable theories in Lukasiewicz innite-valued logic.