Thorn independence in the field of real numbers with a small multiplicative group

TL;DR

This paper characterizes thorn-independence in real fields expanded by dense multiplicative subgroups with specific properties, demonstrating super-rosiness and elimination of imaginaries up to small set codes.

Contribution

It provides a detailed analysis of thorn-independence in real fields with dense subgroups satisfying the Mann property, introducing new structural insights.

Findings

Structures are super-rosy.

Elimination of imaginaries up to small set codes.

Characterization of thorn-independence in these structures.

Abstract

We characterize thorn-independence in a variety of structures, focusing on the field of real numbers expanded by predicate defining a dense multiplicative subgroup, G, satisfying the Mann property and whose pth powers are of finite index in G. We also show such structures are super-rosy and eliminate imaginaries up to codes for small sets.