Abstract
In his paper Definable Valuations (1994) Koenigsmann shows that every field that admits a t-henselian topology is either real closed or separably closed or admits a definable valuation inducing the t-henselian topology. To show this Koenigsmann investigates valuation rings induced by certain (definable) subgroups of the field. The aim of this paper, based on the author’s PhD thesis (Dupont, PhD thesis, University of Konstanz, 2015), is to look at the methods used in Koenigsmann (Definable Valuations, 1994) in greater detail and Koenigsmann (Definable Henselian Valuations, J. Symb. Log. 80(01):85–99, 2015).
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Acknowledgements
I would like to thank Franziska Janke for pointing out the mistake in [16] as well as for several helpful discussions and comments on an early version of this work. Further I would like to thank Salma Kuhlmann and Assaf Hasson for great support and helpful advice while I was conducting the research as well as while I was writing the paper. Also, I would like to thank the referee for thoroughly reading the paper and making some helpful comments.
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Dupont, K. (2017). Definable Valuations Induced by Definable Subgroups. In: Droste, M., Fuchs, L., Goldsmith, B., Strüngmann, L. (eds) Groups, Modules, and Model Theory - Surveys and Recent Developments . Springer, Cham. https://doi.org/10.1007/978-3-319-51718-6_5
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