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Ordered fields dense in their real closure and definable convex valuations

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2021

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https://doi.org/10.1515/forum-2020-0030
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Forum Mathematicum. De Gruyter. 2021, 33(4), pp. 953-972. ISSN 0933-7741. eISSN 1435-5337. Available under: doi: 10.1515/forum-2020-0030

Zusammenfassung

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

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Fachgebiet (DDC)
510 Mathematik

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Regular densely ordered abelian groups, convex subgroups, henselian valuations, almost realclosed fields, Hahn groups and fields, normal integer parts, strongly NIP ordered fields

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ISO 690KRAPP, Lothar Sebastian, Salma KUHLMANN, Gabriel LEHÉRICY, 2021. Ordered fields dense in their real closure and definable convex valuations. In: Forum Mathematicum. De Gruyter. 2021, 33(4), pp. 953-972. ISSN 0933-7741. eISSN 1435-5337. Available under: doi: 10.1515/forum-2020-0030
BibTex
@article{Krapp2021Order-54309,
  year={2021},
  doi={10.1515/forum-2020-0030},
  title={Ordered fields dense in their real closure and definable convex valuations},
  number={4},
  volume={33},
  issn={0933-7741},
  journal={Forum Mathematicum},
  pages={953--972},
  author={Krapp, Lothar Sebastian and Kuhlmann, Salma and Lehéricy, Gabriel}
}
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