Mv-algebras And Partially Cyclically Ordered Groups

Gérard Leloup

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arXiv · 1902.04839

Mv-algebras And Partially Cyclically Ordered Groups

Gérard Leloup

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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.

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BibTeX RIS

Gérard Leloup. 2019-02-13. Mv-algebras And Partially Cyclically Ordered Groups. https://arxiv.org/abs/1902.04839

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