MV-Algebras and Abelian l-Groups: a Fruitful Interaction

  • Vincenzo Marra
  • Daniele Mundici
Part of the Developments in Mathematics book series (DEVM, volume 7)


Introduced by Chang in the late fifties, MV-algebras stand to Łukasiewicz’s infinite-valued propositional logic as boolean algebras stand to the classical propositional calculus. As stated by Chang in his original paper, “MV is supposed to suggest many-valued logics … for want of a better name”. The name has stuck. After some decades of relative quiescency, MV-algebras are today intensely investigated. On the one hand, these algebras find applications in such diverse fields as error-correcting feedback codes and logic-based control theory. On the other hand, MV-algebras are interesting mathematical objects in their own right. The main aim of this paper is to show that the interaction between MV-algebras and lattice-ordered abelian groups — including the timehonored theory of magnitudes — has much to offer, not only to specialists in these two fields, but also to people interested in the fan-theoretic description of toric varieties, and in the K0-theory of AF C*-algebras.


Abelian Group Simplicial Group Boolean Algebra Simplicial Complex Dimension Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Vincenzo Marra
    • 1
  • Daniele Mundici
    • 1
  1. 1.Computer Science DepartmentUniversity of MilanMilanItaly

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