Submission date: 22 October 2020

Abstract:

In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the language of ordered rings. In light of our results, we re-examine the Shelah-Hasson Conjecture (specialised to ordered fields) and provide an example limiting its valuation theoretic conclusions.

Mathematics Subject Classification: 12J15, 03C64, 06F20, 12J10

Keywords and phrases:

Full text arXiv 2010.11832: pdf, ps.