Mv-algebras And Partially Cyclically Ordered Groups
Logic
2019-02-14 v1 Commutative Algebra
Rings and Algebras
Abstract
We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated in terms of MV-algebras. For example, the study of groups together with a cyclic order allows to get a first-order characterization of groups of unimodular complex numbers and of finite cyclic groups. We deduce a characterization of pseudofinite MV-chains and of pseudo-simple MV-chains (i.e. which share the same first-order properties as some simple ones). We can generalize these results to some non-lineraly ordered MV-algebras, for example hyper-archimedean MV-algebras.
Cite
@article{arxiv.1902.04839,
title = {Mv-algebras And Partially Cyclically Ordered Groups},
author = {Gérard Leloup},
journal= {arXiv preprint arXiv:1902.04839},
year = {2019}
}