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arXiv · 2010.11832

Ordered fields dense in their real closure and definable convex valuations

Lothar Sebastian Krapp·Salma Kuhlmann·Gabriel Lehéricy
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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.

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Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy. 2020-10-22. Ordered fields dense in their real closure and definable convex valuations. https://doi.org/10.1515/forum-2020-0030

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