Corpus ID: 119656342

On Strongly NIP Ordered Fields and Definable Convex Valuations

@article{Krapp2018OnSN,
  title={On Strongly NIP Ordered Fields and Definable Convex Valuations},
  author={L. S. Krapp and S. Kuhlmann and Gabriel Leh{\'e}ricy},
  journal={arXiv: Logic},
  year={2018}
}
We investigate what henselian valuations on ordered fields are definable in the language of ordered rings. This leads towards a systematic study of the class of ordered fields which are dense in their real closure. Some results have connections to recent conjectures on definability of henselian valuations in strongly NIP fields. Moreover, we obtain a complete characterisation of strongly NIP almost real closed fields. 
5 Citations
Ordered fields dense in their real closure and definable convex valuations
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Strongly NIP almost real closed fields
  • 2
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Immediately algebraically closed fields
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Definable V-topologies, Henselianity and NIP
  • 12
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References

SHOWING 1-10 OF 25 REFERENCES
Definable valuations induced by multiplicative subgroups and NIP fields
  • 8
  • PDF
Recent Progress on Definability of Henselian Valuations
  • 5
  • PDF
Definable non‐divisible Henselian valuations
  • 17
  • PDF
Some Model Theory for Almost Real Closed Fields
  • 18
  • Highly Influential
  • PDF
Defining coarsenings of valuations
  • 6
  • PDF
DEFINABLE HENSELIAN VALUATIONS
  • 22
  • PDF
Ordered exponential fields
  • 66
Lectures on the model theory of valued fields
  • 24
On dp-minimal fields
  • 31
  • PDF
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