Definably extending partial orders in totally ordered structures

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Mathematical Logic Quarterly 60 (3):205-210 (2014)
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Abstract

We show, for various classes of totally ordered structures, including o‐minimal and weakly o‐minimal structures, that every definable partial order on a subset of extends definably in to a total order. This extends the result proved in for and o‐minimal.

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10.1002/malq.201300047

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References found in this work

Quasi-o-minimal structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
On linearly ordered structures of finite rank.Alf Onshuus & Charles Steinhorn - 2009 - Journal of Mathematical Logic 9 (2):201-239.

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