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  1. Definability of Henselian Valuations by Conditions on the Value Group.Lothar Sebastian Krapp, Salma Kuhlmann & Moritz Link - 2023 - Journal of Symbolic Logic 88 (3):1064-1082.
    Given a Henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any Henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show that in this case, one parameter is optimal in the sense that one cannot obtain definability without parameters. To this end, we present a construction method for (...)
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  • Algebraic and Model Theoretic Properties of O-minimal Exponential Fields.Lothar Sebastian Krapp - 2021 - Bulletin of Symbolic Logic 27 (4):529-530.
    An exponential $\exp $ on an ordered field $$. The structure $$ is then called an ordered exponential field. A linearly ordered structure $$ is called o-minimal if every parametrically definable subset of M is a finite union of points and open intervals of M.The main subject of this thesis is the algebraic and model theoretic examination of o-minimal exponential fields $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp = 1$. This study (...)
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