Extending Partial Orders on o-Minimal Structures to Definable Total Orders

@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}
}
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. 
0 Citations
4 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-4 of 4 references

The axiom of choice, Amsterdam: North Holland

  • T. Jech
  • 1973
1 Excerpt

Similar Papers

Loading similar papers…