Arithmetic of Dedekind cuts of ordered Abelian groups

Details Arithmetic of Dedekind cuts of ordered Abelian groups Arithmetic of Dedekind cuts of ordered Abelian groups

2006-12-10

arxiv.org/abs/math/0612235v3

Annals of Pure and Applied Logic 156 (2008) 210-244

Mathematics

Logic

Scientific paper

10.1016/j.apal.2008.05.001

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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