The Choice Property in tame expansions of o-minimal structures

TL;DR

This paper proves that certain tame expansions of o-minimal structures, including dense pairs of real closed fields, possess the choice property, a weaker form of definable choice, expanding understanding of their logical structure.

Contribution

It establishes the choice property for specific tame expansions of o-minimal structures, notably dense pairs of real closed fields, which was previously unknown.

Findings

Dense pairs of real closed fields have the choice property.

The choice property holds for certain tame expansions of o-minimal structures.

Abstract

We establish the choice property, a weak analogue of definable choice, for certain tame expansions of o-minimal structures. Most noteworthily, dense pairs of real closed fields have this property.