AI

Definably extending partial orders in totally ordered structures

Abstract

We show, for various classes of totally ordered structures \mathcal M=(M,<,...), including o-minimal and weakly o-minimal structures, that every definable partial order on a subset of M^n extends definably in \mathcal M to a total order. This extends the result proved in [5] for n=1 and  \mathcal M o-minimal.