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 Key words: Dedekind cut; Dom; Ordered group Contents 1 Dedekind cuts of ordered sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Dedekind cuts of ordered groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Group extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Doms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1 Basic definitions and facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Sub-doms and dom-homomorphisms . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Type of doms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.4 Associated group and multiplicity . . . . . . . . . . . . . . . . . . . ...

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Antongiulio Fornasiero, Marcello Mamino
• Keywords: APAL 2008, Compatible Families, Dedekind Cuts, Doms