Google Research

Definably extending partial orders in totally ordered structures

Mathematical Logic Quarterly, vol. 60 (2014), pp. 205-210

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.

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