Arithmetic of Dedekind cuts of ordered Abelian groups
Logic
2008-12-16 v3
Abstract
We study the set of Dedekind cuts over a linearly ordered Abelian group as a structure over the language (0,<,+,-). Moreover, we obtain a simple set of axioms for the universal part of the theory of such structures. Finally, we prove that every structure satisfying the given axioms is a sub-structure of the set of cuts over a suitable group.
Cite
@article{arxiv.math/0612235,
title = {Arithmetic of Dedekind cuts of ordered Abelian groups},
author = {Antongiulio Fornasiero and Marcello Mamino},
journal= {arXiv preprint arXiv:math/0612235},
year = {2008}
}