We study Dedekind cuts on ordered Abelian groups. We introduce a monoid structure on them, and we characterise, via a suitable representation theorem, the universal part of the theory of such structures.
Arithmetic of Dedekind cuts of ordered Abelian groups / Fornasiero, Antongiulio; Mamino, Marcello. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - STAMPA. - 156:(2008), pp. 210-244. [10.1016/j.apal.2008.05.001]
Arithmetic of Dedekind cuts of ordered Abelian groups
Fornasiero, Antongiulio;
2008
Abstract
We study Dedekind cuts on ordered Abelian groups. We introduce a monoid structure on them, and we characterise, via a suitable representation theorem, the universal part of the theory of such structures.
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