Arithmetic of Dedekind cuts of ordered Abelian groups

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Arithmetic of Dedekind cuts of ordered Abelian groups

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. MSC: 06F05; 06F20

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Arithmetic of Dedekind cuts on ordered Abelian groups

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. MSC: 06F05; 06F20

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A Dedekind cut of an ordered abelian group G is a pair (X, Y) of nonempty subsets of G where Y=G−X and every member of X precedes every member of Y. A Dedekind cut (X, Y) is said to be continuous if X has a greatest member or Y has a least member, but not both; if every Dedekind cut of G is a continuous cut, G is said to be (Dedekind) continuous. The ordered abelian group R of real numbers is, ...

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Characterizing automorphism groups of ordered abelian groups

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ژورنال

عنوان ژورنال: Annals of Pure and Applied Logic

سال: 2008

ISSN: 0168-0072

DOI: 10.1016/j.apal.2008.05.001