Generalized halfspaces in dimension groups

doi:10.1016/j.apal.2007.10.009

Annals of Pure and Applied Logic

Volume 154, Issue 1, May 2008, Pages 8-26

https://doi.org/10.1016/j.apal.2007.10.009 Get rights and content

Under an Elsevier user license

open archive

Abstract

In a dimension group, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The dimension groups obeying a stronger version of this result, true in dense Archimedean ordered groups, are characterized algebraically and provided with a simple set of axioms.

MSC

primary

03C64

secondary

06F20

15A39

Keywords

Ordered Abelian group

Dense regular group

Dimension group

Quantifier elimination