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Logic Journal of IGPL Advance Access originally published online on July 4, 2009
Logic Journal of IGPL 2009 17(4):395-412; doi:10.1093/jigpal/jzp017
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The category of MV-pairs

Antonio Di Nola

Department of Mathematics and Information Sciences, Università degli Studi di Salerno, Via Ponte Don Melillo, 84084 Fisciano (Salerno), Italy.
E-mail: adinola{at}unisa.it

Michal Holcapek

Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 33 Ostrava 1, Czech Republic.
E-mail: michal.holcapek{at}osu.cz

Gejza Jenca

Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Radlinskéeho 11, Bratislava 813 68, Slovak Republic.
E-mail: gejza.jenca{at}stuba.sk


  Abstract

An MV-pair is a pair (B,G), where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain condition. Recently it was proved by one of the authors that for an MV-pair (B,G), ~G is an effect-algebraic congruence and B/~G is an MV-algebra. Moreover, every MV-algebra M can be represented by an MV-pair in this way.

In this paper we show that one can define a suitable category of MV-pairs in such a way that there exist a faithful functor from the category of MV-algebras to the aforementioned category and a functor in the reversed direction.

Key Words: MV-algebra • Boolean algebra • MV-pair


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