## Discrete o-minimal structures

- Anand Pillay, Charles Steinhorn
- Ann. Pure Appl. Logic
- 1987

@article{Macpherson1997ExtendingPO, title={Extending Partial Orders on o-Minimal Structures to Definable Total Orders}, author={Dugald Macpherson and Charles Steinhorn}, journal={Math. Log. Q.}, year={1997}, volume={43}, pages={456-464} }

- Published 1997 in Math. Log. Q.
DOI:10.1002/malq.19970430403

In this note we answer a question raised by John Truss. He asked if every definable partial ordering in an o-minimal structure can be extended to a definable total order. His question is motivated by analogy with the Order Extension Principle, a weak choice-like axiom of interest to set theorists, which asserts that every partial ordering of a set can be extended to a total order of the set (see [1], for example). We prove the following theorem.

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