Dependent Pairs

TL;DR

This paper proves that specific pairs of ordered structures, including o-minimal structures and real fields with certain subgroups, are dependent, expanding understanding of their logical properties.

Contribution

It establishes dependence for pairs of structures like dense o-minimal pairs and real fields with subgroups having the Mann property, regardless of density.

Findings

Dependent pairs of dense and tame o-minimal structures

Dependence of real fields with multiplicative subgroups with Mann property

Applicability to both dense and discrete subgroups

Abstract

We prove that certain pairs of ordered structures are dependent. Among these structures are dense and tame pairs of o-minimal structures and further the real field with a multiplicative subgroup with the Mann property, regardless of whether it is dense or discrete.