Arithmetic of Dedekind cuts of ordered Abelian groups

Annals of Pure and Applied Logic 156 (2):210-244 (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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DOI 10.1016/j.apal.2008.05.001
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On Completing Ordered Fields.Dana Scott - 1969 - In W. A. J. Luxemburg (ed.), Applications of Model Theory to Algebra, Analysis, and Probability. New York: Holt, Rinehart and Winston. pp. 274--278.

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