On definable Skolem functions and trichotomy

Abstract

In this paper we give an explicit characterization of o-minimal structures with definable Skolem functions/definable choice. Such structures are, after naming finitely many elements from the prime model, a union of finitely many trivial points each defined over $\varnothing$ and finitely many open intervals each a union of a $\varnothing$-definable family of group-intervals with fixed positive elements.