Definable choice for a class of weakly o-minimal theories

Abstract

Given an o-minimal structure $\mathcal{M}$ with a group operation, we show that for a properly convex subset $U$, the theory of the expanded structure ${\mathcal{M}}^{\prime }=(\mathcal{M},U)$ has definable Skolem functions precisely when ${\mathcal{M}}^{\prime }$ is valuational. As a corollary, we get an elementary proof that the theory of any such ${\mathcal{M}}^{\prime }$ does not satisfy definable choice.

11 pages

Cited by in corpus (1)

• On definable Skolem functions in weakly o-minimal non-valuational structures