Definable Valuations Induced by Definable Subgroups

Abstract

In [Koe94] 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 authors PhD thesis [Dup15], is to look at the methods used in [Koe94] in greater detail and correct a mistake in the original paper based on [JK15a].