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Arithmetic of Dedekind cuts of ordered Abelian groups

Antongiulio Fornasiero·Marcello Mamino
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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.

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BibTeXRIS

Antongiulio Fornasiero, Marcello Mamino. 2008-12-16. Arithmetic of Dedekind cuts of ordered Abelian groups. https://doi.org/10.1016/j.apal.2008.05.001

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