6533b857fe1ef96bd12b4443
RESEARCH PRODUCT
Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras
Luca SpadaVincenzo Marrasubject
Fundamental groupPure mathematicsUnificationŁukasiewicz logic; Unification; Projective MV-algebras; Rational polyhedra; Fundamental group; Covering spaceLogicCovering spaceDuality (mathematics)Projective MV-algebrasMV-algebraCovering spaceŁukasiewicz logicRational polyhedraAlgebraAlgebraic semanticsUnificationVariety (universal algebra)Algebraic numberŁukasiewicz logicMathematicsdescription
AbstractWe prove that the unification type of Łukasiewicz (infinite-valued propositional) logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the background to such diverse tools. In particular, we offer a detailed proof of the duality theorem for finitely presented MV-algebras and rational polyhedra—a fundamental result that, albeit known to specialists, seems to appear in print here for the first time.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-03-01 | Annals of Pure and Applied Logic |