MV-algebras, infinite dimensional polyhedra, and natural dualities
Rings and Algebras
2016-03-04 v1 Logic
Abstract
We connect the dual adjunction between MV-algebras and Tychonoff spaces with the general theory of natural dualities, and provide a number of applications. In doing so, we simplify the aforementioned construction by observing that there is no need of using presentations of MV-algebras in order to obtain the adjunction. We also provide a description of the dual maps that is intrinsically geometric, and thus avoids the syntactic notion of definable map. Finally, we apply these results to better explain the relation between semisimple tensor products and coproducts of MV-algebras, and we extend beyond the finitely generated case the characterisations of strongly semisimple and polyhedral MV-algebras.
Keywords
Cite
@article{arxiv.1603.01005,
title = {MV-algebras, infinite dimensional polyhedra, and natural dualities},
author = {Leonardo M. Cabrer and Luca Spada},
journal= {arXiv preprint arXiv:1603.01005},
year = {2016}
}
Comments
15 pages