Geometry of Robinson joint consistency in Lukasiewicz logic

Abstract

We establish the Robinson joint consistency theorem for the infinitevalued propositional logic of Lukasiewicz. As a corollary we easily obtain the amalgamation property for MV-algebras the algebras of Lukasiewicz logic: all pre-existing proofs of this latter result make essential use of Pierce amalgamation theorem for abelian lattice-ordered groups (with strong unit) together with the categorical equivalence $\Gamma$ between these groups and MV-algebras. Our main tools are elementary and geometric.

Published: Annals of Pure and Applied Logic, 147 (2007), 1-22.