Submission date: 8 May 2015.

Abstract:

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

Mathematics Subject Classification: 03C64

Keywords and phrases: model theory, Skolem functions, definable choice, o-minimal, weakly o-minimal

Full text arXiv 1505.02147: pdf, ps.