Ordered fields dense in their real closure and definable convex valuations-Reference-Cited by-同舟云学术

Ordered fields dense in their real closure and definable convex valuations

Published:2021-05-19 Issue:4 Volume:33 Page:953-972
ISSN:1435-5337
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Krapp Lothar Sebastian¹^ORCID,Kuhlmann Salma¹,Lehéricy Gabriel²

Affiliation:

1. Fachbereich Mathematik und Statistik , Universität Konstanz , 78457 Konstanz , Germany

2. Fachbereich Mathematik und Statistik , Universität Konstanz , 78457 Konstanz , Germany ; and École supérieure d’ingénieurs Léonard-de-Vinci, Pôle Universitaire Léonard de Vinci, 92 916 Paris La Défense Cedex, France

Abstract

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 (specialized to ordered fields) and provide an example limiting its valuation-theoretic conclusions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2020-0030/pdf

Reference30 articles.

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