English

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.

Keywords

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}
}
R2 v1 2026-07-22T17:47:35.667Z