A monotonicity theorem for dp-minimal densely ordered groups

Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inpminimality and prove that in an inp-minimal densely ordered group, every denable unary function is a union of nitely many continuous locally monotonic functions (Theorem 3.2).

• Type: Journal
• Year: 2010
• Where: JSYML
• Authors: John Goodrick
• Keywords: Densely Ordered, JSYML 2010, Ordered Group, Weakly O-minimal Theory