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.
- Pub Date:
- October 2018
- Mathematics - Logic
- 31 pages. In this fourth and final version, we have added Observation 7.3, modified the abstract, reworked the introduction, and corrected grammar as well as typos