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

TL;DR

This paper investigates the existence of definable Skolem functions in weakly o-minimal non-valuational structures, showing they generally do not exist but that these structures eliminate imaginaries up to definable cuts, and introduces new examples.

Contribution

It demonstrates the non-existence of definable Skolem functions in known examples and provides new structures, while also establishing elimination of imaginaries up to definable cuts.

Findings

Weakly o-minimal non-valuational structures lack definable Skolem functions.

Such structures eliminate imaginaries up to definable families of cuts.

New examples of weakly o-minimal non-valuational structures are provided.

Abstract

We prove that all known examples of weakly o-minimal non-valuational structures have no definable Skolem functions. We show, however, that such structures eliminate imaginaries up to (definable families of) definable cuts. Along the way we give some new examples of weakly o-minimal non-valuational structures.